Metabolism in Goldfish Database Section Assignment
Metabolism in Goldfish Database Section Assignment
Before You Start the Writing Assignment
Explore the database provided in the Metabolism Database section (https://ls23l.lscore.ucla.edu/METABOLISM/?quarter=…)
You can select any term (i.e. Winter 2020) and any section (i.e. 1G) to write your report on. When you select a term and a section, you will be presented with two data sets, one from each bench in the wet lab classroom. Select one of these for your report. You will also be able to “View All Data”, which will pool the data for the entire quarter you are viewing, or from every quarter to date. This is OPTIONAL and must be in addition to (but not instead of) your chosen bench’s data. Metabolism in Goldfish Database Section Assignment
Based on this lab you will complete the second scientific writing
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Lab Manual (R): Metabolism in Goldfish
Propose a testable hypothesis related to metabolic
Design an appropriate experiment for testing your hypothesis and collect the relevant data, using
Analyze and present your results and draw a conclusion concerning your hypothesis in a written scientific style research
All living things carry out metabolic processes, where metabolism is defined as the total chemical activity within that organism. The chemical activity which occurs is the sum of all anabolic and catabolic processes. Anabolic pathways synthesize important chemical building blocks, whereas catabolic pathways serve to break down molecules. The energy required to perform these reactions is obtained through respiration. Through respiration, organisms obtain oxygen, whose rate can then be measured to correlate with metabolic rate. Metabolic rate, however, can also be influenced by an organism’s body temperature.
In lab this week, you will explore how different variables affect the oxygen consumption rate in goldfish. Goldfish are poikilothermic organisms whose body temperature changes when the environmental temperature changes, thus making the organism’s metabolic rate easier to manipulate. Each group will generate a hypothesis about your assigned environmental effect on the metabolic rates in goldfish. You will then design an appropriate experiment for testing the hypothesis. Finally, you will be given a set of data to analyze using a paired t-test. (This test is different from the unpaired test used in the Scientific Methodology and the MIT lab. See Appendix C for a detailed example.)
This lab will be the basis of your second writing assignment. You will be given an environmental variable and its accompanying data in class. However, you are free to choose a different environmental variable when forming a hypothesis for your paper. You will use the metabolism database to test your hypothesis. You will analyze the results, as well as provide interpretations and conclusions for the experiment, in your paper.
Please note: This is the unedited laboratory manual for the LS23L metabolism lab. You are being given the entire text in order to facilitate your writing process for Writing Assignment #2. Dr. Pfluegl will provide supplemental instructions on CCLE for how he would like you to complete this remote lab. Metabolism in Goldfish Database Section Assignment
Experimental Materials Used in the LS23L Wet Lab
Chamber with sensor
dH2O wash bottle
Fish water carboy
The Computer Program
This lab exercise has an online tutorial to guide you as you formulate your hypotheses and predictions and learn about experimental strategies by which to test them. It is best to begin the lab by browsing through this tutorial. This will help you think of ideas for your writing assignment. The tutorial can be accessed from our lab website (https://ls23l.lscore.ucla.edu/TUTORIAL/?METABOLISM).
The Metabolism Chambers
You will be conducting your experiment(s) using goldfish in a small oxygen chamber. The oxygen chamber has a built-in probe that provides a continuously updated measure of the oxygen concentration in the chamber’s water. Because it is a closed system, the chamber will contain less and less oxygen as the fish utilize the oxygen that was initially in the water.
Preparing the Metabolism Chambers for Experiments
Keeping the Water Oxygenated for the Fish
For each of your trials the oxygen chamber should contain a total of 400 milliliters fish water to ensure that the fish have enough oxygen. Because oxygen is depleted over the course of a trial, you must refresh the water between each trial. To do this, leave the fish in the chamber and
gently pour off at least 100 milliliters of the oxygen-depleted water into your beaker. Then add the same volume of fresh fish water back into the chamber. If your experimental variable is dissolved in fish water, you can use fish water treated with your variable instead of plain fish water.
From the computer desktop, open up the LoggerLite file called LoggerLite-metabolism expt.
PLEASE NOTE: The dissolved oxygen probe needs to warm up for at least 10 minutes before you acquire data. Make sure that the probe is connected and then open up the LoggerLite- metabolism expt file BEFORE going to get your fish. Leave the program open to let the probe warm up. If you close the program, you will need to warm the probe up for another 10 minutes before resuming your experiment.
To Run the Experiment:
Add the specimen and sufficient treated water to the oxygen chamber and secure the plunger Use caution in trying to eliminate any bubbles inside the chamber. Give the fish two or three minutes to acclimate before beginning to collect data.
To begin recording data, click on the large green arrow button with the word “Collect.” You will see the quantity of dissolved oxygen change over time.
Use this data to create a graph in Excel or Google Sheets
During your experiments, the oxygen probe will be assessing the oxygen concentration in mg/L. As more and more oxygen is used by the fish, the value will drop. The LoggerLite software will produce a mini-spreadsheet, continuously updated, that indicates the actual oxygen concentration in the water. For each trial you will need to graph these data points and add a trendline. The slope of the line will indicate the change in oxygen concentration over time for that trial.
Figure 1. Example of LoggerLite data exported to Excel graphed and annotated.
Designing an Experiment – Metabolism in Goldfish Database Section Assignment
What Sorts of Questions Can You Ask?
In the lab you will have access to materials that will allow you to alter the water temperature, the light intensity, and other variables. There are some experiments you can do using chemical manipulations. These manipulations have the potential to harm fish; therefore, the following guidelines for maximum dosages must be followed. Use the specially prepared fish water AT ALL TIMES. Ordinary tap water contains chlorine, which will kill fish.
To save time and trouble, whenever you choose a variable that involves changing the chemical nature of the water for the fish, you should use half the treated water in the first trial and save half for use in the second trial. In doing so you will not need to spend time to prepare the test water again.
Salinity: The maximum amount of salts that goldfish should be exposed to is 10 ppt (parts per thousand), which is the concentration of seawater your TA will provide.
Temperature: The maximum level of temperature change allowed is ±10℃. You can choose either the colder water temperature or warmer water temperature as your experimental group. The control is room temperature fish water.
Lighting: There are two variables that your group can choose, either with extra light or with black plastic covering the test chamber. The control is the normal ambient light.
Caffeine: 50 mg of a caffeine tablet will be dissolved in fish water before being transferred into test chamber. Use half of the treated water for the first trial and half for the second.
Nicotine: 1.5 g of tobacco is infused in fish water. Use half of the treated water for the first trial and half for the second.
Remember that you are not restricted to these experiments and are encouraged to use your imagination (while avoiding cruelty and being intrusive to the goldfish). Metabolism in Goldfish Database Section Assignment
What Will A Good Experiment Entail?
It is critical that you propose a hypothesis that you can answer definitively. Do not rush into data collection before carefully considering how testable your hypothesis is (especially given the time constraints you are working under in the lab).
Should the fish be the same size or different sizes?
Should the control fish be the same fish as in the experimental group?
Should the control or experimental measurements be made first?
What sort of manipulation will you be making?
Can you imagine all possible results? Do you know how you will interpret them?
Are you unintentionally altering more than one variable at a time?
Is your experiment interesting? For example, we all know that putting a stir bar into the chamber and turning it up to a high speed would cause your fish to increase their metabolic rates. Try to imagine an experiment with two features: (1) you don’t know what the results will be, and (2) you (and your TA) would like to know what the results will
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Figure 2. Pictorial representation of a good experimental set-up. Note that while two trials are performed, the same two fish are used for the control group and experimental group in each trial.
Figure 3. Pictorial representation of the student groups. Each classroom “bench” (shown here in blue), will have four groups who decide on and use the same experimental condition during their experiment (i.e. Condition 1 is darkness and Condition 2 is salinity).
How Can You Anticipate Potential Problems?
Create a flowchart describing the order in which you will perform the various parts of your experiment, from hypothesis to experimental setup and execution, to data analysis, and the components of each of these parts. A good flowchart will help you anticipate sources of error and, thus, organize your experiment to minimize problems. (See Figure 9 for an example flowchart.) Consider the following as you develop your own flowchart:
a. Try to envision how you will analyze your data before beginning the experiment.
What comparisons will you make?
What values will you graph?
How large a sample size do you need? That is, how many trials do you need to run in order to know that the effect you observe is repeatable, and, therefore, likely real? This is particularly important if you intend to test differences between control and experimental treatments statistically. If so, have you planned enough trials to adequately estimate means and standard deviations?
What graphs do you want in your research paper?
b. Try to imagine any criticisms that a reader of your paper might have and address them.
Have you quantified oxygen use in a way that makes sense? Which makes more sense for your experiment: rate of oxygen usage (i.e., the slope of the line plotting oxygen concentration vs. time), absolute change in oxygen use over some fixed period of time, or oxygen consumption per fish (or per gram of fish) per unit time?
Have you used the proper control group, given the way you chose to quantify oxygen use?
Have you controlled all extraneous variables such that the treatment and control conditions differ only with respect to the variable under investigation?
Does the amount of water in the chamber affect your measurements of oxygen consumption?
Analyzing and Presenting Your Data – Metabolism in Goldfish Database Section Assignment
What Sort of Data Output Do You Get from the LoggerLite Program?
You will get a table of data with two columns. The first column is the time in seconds and the second column is the oxygen concentration in the water during that run. After each run, you can import the data into Excel to produce a linear regression equation and chart. Remember to record all data after each run.
How Can You Present This Data in an Interesting Way?
Use the raw data. For example, a group of students attempted to test the null hypothesis that oxygen consumption rates of male and female fish do not differ. Two groups of fish were enclosed in the chamber separately; one consisted of three female fish and the other of three male fish. Oxygen consumption rates of each group of fish were measured only once. That is, only a single trial per group of fish was performed. The raw data for this experiment included oxygen concentrations through time for each group. The students entered their raw data (the time and oxygen concentration from each trial) into a spreadsheet program (such as Excel), made a scatter plot, and fit a best-fit trendline like the one seen in Figure 4. Is this experiment well controlled? Can an observed difference in oxygen consumption rates between males and females be attributed unquestionably to differences in sex? Metabolism in Goldfish Database Section Assignment
What other factors might account for an apparent difference in oxygen consumption rates in this experiment? For example, were the males and females exactly the same size in both groups? What effect might size have on oxygen consumption rates? Can these effects be distinguished from the hypothesized effects of sex in this case?
Figure 4. Metabolic rates of male and female goldfish measured as oxygen consumption. Each line reflects the collective metabolic rates of three fish (n = 1 for each treatment).
The students performed a simple analysis of the data by calculating the rate of oxygen consumption as oxygen lost per hour [(O2 time begin – O2 time end)/total time]. Data such as this can be presented using a column, bar, or scatter graph. See Figure 5.
Figure 5. Metabolic rates of male and female goldfish measured as oxygen consumption and presented as average rate of oxygen consumption per hour. Each bar represents the collective metabolic rates of three fish (n = 1 for each treatment).
The students used the slopes of the linear regression lines calculated by the LoggerLite program (Figure 6). In their lab report, the students discussed what these differences in slopes meant, e.g., what did a large negative slope mean biologically? How were the slopes calculated? If you use LoggerLite to fit a curve to all data collected, the absolute value of these slopes should be the same as those values calculated in Alternative 2. Why? Hint: How do you calculate the slope of a line? However, if you use LoggerLite to fit a curve to only a portion of the data, the values may differ. Why?
Figure 6. Metabolic rates of male and female goldfish measured as oxygen consumption and presented as the slope (mgO2 per liter per hour). Each bar represents the collective metabolic rates of three fish (n = 1 for each treatment). Metabolism in Goldfish Database Section Assignment
Students performed multiple trials within each of the two treatments (female and male). This enabled them to calculate the average rate of oxygen loss across trials and then compare these averages between treatments. To do this, they measured the oxygen consumption rates of four different groups of female fish and four different groups of male fish; each group consisted of three fish. Each different group of three fish constitutes a “trial.” This produced an n = 4, i.e., a sample size of four trials per treatment. (A “treatment” is the condition of being male or female.)
They then calculated the rate of oxygen lost per hour (as in Alternative 2) for each trial individually and averaged these values for each treatment. The results are presented in Figure
What are the advantages of repeated trials over single runs (as in Alternatives 1, 2, and 3) with respect to the confidence you have in your results? The error bars presented in Figure 7 are standard deviations, and, as such, reflect the variability in metabolic rates among trials within a treatment-that is, how much oxygen consumption rates differed between different groups of fish within a treatment.
Figure 7. Metabolic rates of male and female goldfish measured as oxygen consumption and presented as average rate of oxygen consumption per hour (± standard deviation, n = 4 for each treatment).
The students controlled for differences in the size (weight) of fish among trials and between treatments by calculating the cate of oxygen loss per kilogram of fish. To do this, they divided the rate of oxygen loss (as calculated in Alternatives 2 and 4) by the total weight of the fish in each trial (four trials per treatment as described in Alternative 4). They then averaged these weight-standardized oxygen consumption rates among trials within each treatment as in Alternative 4. Data such as these can be presented as a column, bar, or scatter graph. The students’ results are presented in Figure 8.
Compare the results presented in Figure 8 to those in previous figures. Did standardizing for differences in fish weight alter the interpretation of the results of this experiment? Why or why not?
Figure 9. Example flowchart of experimental design and execution.
Return fish ONLY (no used fish water) to the original
Follow the instructions for the chamber posted at each
Make sure the chamber has enough dH2O in it to submerge the
Return all items to their original places and clean up your
Log off your
The Scientific Style Research Paper for Metabolism
(Refer to Appendix A for an example.)
For this assignment, you will learn to write the second half of a scientific research paper. Because we cannot run the actual lab this quarter, you will be writing your text based on data chosen from the metabolism database, which contains all LS23L data from past quarters. You will form a hypothesis and then look at the metabolism database to find a lab section that performed the experiment with your environmental variable. Each lab section has two benches that performed two different experiments (Figure 3). For example, if you look at section 1A from Fall 2019, one bench chose cold water and one bench chose nicotine to run their experiment with. You can choose any variable that is of interest to you. If you would like, you may also write about data for your variable from a broader time period (i.e., the entire quarter in which your chosen section was held), but this must be IN ADDITION TO the data for your chosen section, so in this case you would need to present two p-values (one for your bench data, one for the broader time period). All data are available on our website and the link is provided in the “Metabolism in Goldfish” section on CCLE. For specific guidelines and deadlines, please refer to the Writing Assignment #2 rubric and Dr. Pfluegl’s presentation, both posted on the LS23L CCLE site. Metabolism in Goldfish Database Section Assignment
Short, concise, and relevant.
INTRODUCTION – Metabolism in Goldfish Database Section Assignment
You will not be writing an introduction section for this assignment. Instead, simply state your hypotheses (null and alternative).
MATERIALS AND METHODS
You will not be writing a materials and methods section for this assignment. Instead, simply state what statistical test was used to analyze your data.
Describe the results of the experiment, including your statistical results. You should never present raw data (individual measurements or the results of individual trials, for example) in a scientific paper. When deciding what data to include, think about what you would find useful if you were reading someone else’s study. Keep in mind that the study you are conducting is very small, but many research studies have hundreds of subjects. Would you want to have to read through the weight of hundreds of individual subjects? Would that be useful to you? Wouldn’t it be more helpful to know the average and/or median weight? This is why we use statistics instead of raw data. Keep in mind that you may not see a statistically significant difference and that is fine. While you must include your p-value statistic here, it is not appropriate to draw interpretations in the results section. That is reserved for the discussion section.
It can be useful to provide figures in your results section, to help present your data in a visual way. If you choose to include a figure (this is optional for the assignment) make sure that you have labeled it properly and that you reference it in the text.
Make sure you include correct units for your data throughout. (See Appendix A for more information.)
Was the null hypothesis rejected? Discuss the results and their implications. Do your findings agree with previous research? You must find a relevant scientific paper and cite it here, relating your results to the work that has already been done in this area. Did you see any inconsistencies in the data? If so, what might have caused them?
What is the next step? Describe thoughtful suggestions for further research that could extend your findings. Bear in mind that while increasing the sample size might be useful to improve the power of a study, this is not considered a thoughtful suggestion for further research. Be more creative! You aren’t limited to the equipment we had in lab when considering future experiments.
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Appendix A: Tips on Lab Research Paper Writing
Title of the Research Paper
Your title should be short but descriptive. A good title gives a clear indication of what a paper is about, so that it can easily be found by other scientists. It should not be overly wordy, but it needs to have sufficient detail that someone scanning titles will know the topic. Titles should never be catchy or colloquial!
A scientific paper does not require a “hook” or lead in. Your goal should be to present the facts clearly and objectively using a professional tone. Assume your audience is another scientist who is generally well informed but not an expert on this particular topic. Scientific writing rarely uses first person point of view. Never use “I” statements in your research papers, although it is acceptable to use “we” statements sparingly. Since you will be writing about a study that has already been conducted, make sure that you are using past tense throughout your paper. Briefly describe the background and give some information on previous research that has been done in this area. As a UCLA student you have access to the PubMed database while you are on campus (or via VPN if you are off campus). If you are having trouble searching for journal articles you can contact the library for remote help (https://www.library.ucla.edu/news/remote-resources-general-information-ucla-library-users). Make sure to cite your sources appropriately by stating the author name and publication year in parentheses (Pfluegl 2018). Remember that you need to cite any sources you consulted while writing your paper, otherwise it is considered plagiarism. If you need a review on how to properly use sources you can refer to the Annotated Scientific Paper on our CCLE site.
The background information and the previous work should lead you to a “knowledge gap” – a question that has not been fully answered and needs more research, which you seek
to address in your research study. This is the rationale for your study. Think about this logically
– if numerous studies already exist showing a definitive link between caffeine and improvement in short term memory, is it interesting to focus your study on that question? Would such a study be likely to get funding? Instead, think about areas that have not been fully explored yet that might be interesting. What questions are raised when you read the previous research? Maybe research has been done on one population but not on others. Might the effect be different at different ages, or in different groups of people? How can you build on what we already know and further scientific knowledge?
Towards the end of your introduction you must state your hypothesis, along with your null hypothesis. A null hypothesis assumes that there is no difference between a control group and an experimental group. Although most published scientific papers will only state the
hypothesis (sometimes called the alternative or experimental hypothesis), knowing that the informed audience will infer the null hypothesis, in LS23L we require that you state both the null and alternative hypotheses for learning purposes. Formulating a good hypothesis is a critical part of scientific thinking. A strong hypothesis must be specific and testable.
Materials and Methods
This section is a summary of the techniques, mechanisms, statistic methodology, and all the materials used. It should be sufficient to enable another scientist to replicate your experiment. Remember that your audience is another scientist who is generally well informed but not an expert on your experiment. When deciding what to include, consider the information you would find in a recipe. You want to include all necessary materials and important procedures, but you can assume your reader will be able to figure out how to turn on the stove. Likewise, you would not want to spend time explaining things that are specific to your lab, like which shelf the beakers are located on, since this information would be useless to a researcher working in a different lab. Unlike a recipe, however, the materials and methods section must be written in prose (paragraph form) and cannot use lists, bullet points, or flowcharts in lieu of text (although flowcharts are sometimes used in addition to text, if they are helpful).
Make sure to include information about your sample population and what type of statistical test you are using to analyze your data. Do not include any actual results in this section.
Results – Metabolism in Goldfish Database Section Assignment
What did your experiment reveal? This section should contain a straightforward report of the statistical data. Do not interpret the data or draw any conclusions.
You should never present raw data (individual measurements or the results of individual trials, for example) in a scientific paper. When deciding what data to include, think about what you would find useful if you were reading someone else’s study. Keep in mind that the studies you are conducting in LS23L are generally small, but many research studies have hundreds of subjects. Would you want to have to read through the weight of hundreds of individual subjects or the results of hundreds of individual trials? Would that be useful to you? Wouldn’t it be more helpful to know the average and/or median? This is why we use statistics instead of raw data.
Anytime you include a number, first consider what information this is giving to your reader. You want to make sure that you include the results of any statistical tests you ran to analyze your data.
Figures are often used in the results section. In LS23L you are not required to include figures, but they can sometimes be helpful to present your data to your audience. If you do include figures, make sure that you spend some time determining what type of figure best describes your data. This may involve graphs, bar charts, or tables. Label your axes and data clearly. Give your figures legends that include a brief description of the material presented in the figure, including sample size. Tables should be labeled with a title; a simple statement describing the contents. Avoid common errors that make your figures needlessly complicated such as using a three-dimensional bar graph if you are only presenting two dimensions of data. Figures should not be included in lieu of text. All of your figures should make sense without reference to the text. However, any figures included must be referenced somewhere in the text by using the following citation format (Figure 1).
Interpret your results in this section. Support your conclusions with reference to the data you collected. How did the measurements on your experimental group(s) differ from those of your control groups? What conclusions can you draw from your data? What is the status of your hypothesis following the experiment, based on the statistical tests you conducted? Do your data suggest any interesting subsequent experiments for further, more robust testing of your hypothesis? Do they give rise to additional hypotheses? What directions should future experiments take?
Keep in mind that an experiment is not a failure just because you didn’t have statistically significant results. Sometimes the lack of relationship between two variables is more interesting than a relationship. Whether or not you saw a significant difference, you have gained valuable information and you should be able to discuss it in a meaningful way.
Do not spend the majority of your discussion going over possible sources of error in your experiment just because you did not see the results you expected. If there were inconsistencies in your data that you feel were caused by experimental errors you should certainly address them, but you should not try to explain your results away just because they do not agree with your expectations.
How do your findings align with the current research in this area? You should have already done a literature search before conducting your study, when formulating your hypotheses. Revisit that research now, and relate your findings to the previous work. Does your study agree with similar work that has been done elsewhere? Does your study cast new light on the current understanding of the topic? Often, this leads to additional questions. What direction would you explore next? Include thoughtful suggestions for future research projects here. Metabolism in Goldfish Database Section Assignment
Make sure to review your paper after you have written it. Check carefully for unclear phrases, typos or grammatical errors that may make it difficult for your reader to understand what you have written. Although scientific papers must be factual and objective, they do not
need to be overly complicated and using unnecessarily complex language will make your paper more difficult to read.
In LS23L we use the following citation style, which is modified from standard APA guidelines. Here are a few examples of the citation style. For any citations not covered here, you can refer to this website to determine how to cite them: https://owl.purdue.edu/owl/research_and_citation/apa_style/apa_formatting_and_style_guid e/general_format.html
Most journals have strict citation requirements. In LS23L we are mostly concerned with making sure that you learn to cite sources and use a somewhat consistent method to make it easy for your classmates to read your text. We will not dock points if your citation style has minor errors, as long as you provide citations.
Journal article, one author:
Pfluegl, Gaston. “Proper Citation of Sources.” Annals of Scientific Writing, vol. 15, 2018, pp. 41 –
Cite in text as (Pfluegl 2018)
Journal article, two authors:
Laing, Jennifer, and Warwick Frost. “Unintentional Plagiarism and Serious Implications for the Scientific Community.” International Journal of Scientific Communications, vol. 29, 2016, pp. 261 – 270.
Cite in text as (Laing and Frost 2016)
Journal article, with three or more authors:
Chen, Jamie, et. al. “Examination of Collaborative Works and Proper Citations.” Journal of
American Scientific Studies, vol. 18, 2017, pp. 134 – 135. Cite in text as (Chen et. al. 2017)
Cornell University Library. “Citation Management.” Cornell University Library. http://www.library.cornell.edu/resrch/mla
Cite in text as (“Citation Management”) – note that websites have a different citation format, since you generally do not know the author or the year it was written, you include the title of the article in quotes.
Metabolism in Goldfish Database Section Assignment Appendix C: Example of a Two-Tailed, Paired t-Test Calculation
(Used in Metabolism of Goldfish)
This hypothetical example compares the resting heart rate measured in beats per minute (bpm) of subjects before and after caffeine ingestion. This particular example is a two tailed- paired t- test, like the one used in the Metabolism of Goldfish lab. A two-tailed test looks at differences in either direction. The test is paired (also called dependent) because each measurement in data set 1 has a corresponding measurement in data set 2. Paired t-tests are often used when looking at before and after data, like those below, but there are other situation in which they are appropriate. For example, if you wanted to look for a correlation between the IQ of mothers and their children, paired sample measurements could be very useful. Unlike an unpaired t-test, a paired test looks at the differences between each pair of measurements – all descriptive statistics are calculated for the differences between the paired measurements, rather than for each data set as we saw in the example in Appendix B (included with the MIT lab manual chapter). If used appropriately, the paired t-test can be more sensitive to differences than the unpaired t-test. Metabolism in Goldfish Database Section Assignment
Experimental hypothesis: Subjects’ heart rates change after the ingestion of caffeine.
Null hypothesis: There is no difference in the subjects’ heart rates before and after ingesting
= | ̅| = |−2.9| = 2.2
To find your p-value, you would loop up a t-value of 2.2 with 6 degrees of freedom (we do not add the degrees of freedom in a paired t-test because we are only interested in the number of paired measurements) in a table like the one used in the Scientific Methodology and the MIT lab.
Table C-1. Critical Values for Students’ t-Distribution.
The p-value for the example is between 0.08 and 0.06. Do we accept or reject the null hypothesis? Metabolism in Goldfish Database Section Assignment