You are the editor of a journal. A research team has submitted a paper to you. Their hypothesis is that daily consumption of a product, MaxTreme WonderLiquid, will produce an increase in endurance as measured by repetitions of a strength task. The methods section is below: We began by obtaining a baseline measurement of each subject's performance on the arm strength task. This involved the subject placing their right elbow on the table, grasping the handle, and moving the lever through a 45° arc to the left once every three seconds. A tone sounded every three seconds, indicating when the subject should begin moving the lever, and a green light went on each time the subject moved the lever to the correct distance, allowing the subject to know when he or she could allow the lever to return to the rest position. Resistance in the lever was kept constant for all trials and all subjects. The number of successful repetitions which each subject could complete prior to fatigue was recorded as the "baseline" measurement. Subjects returned for further testing each day for the next week. Testing always took place at 8:00 am. On each day, prior to completing the same task described above, the subjects were given one 16-ounce bottle of MaxTreme WonderLiquid, which they consumed in two minutes. All bottles were kept at the same temperature (10° Celsius). Subjects then completed the task, with the number of repetitions recorded as that day's score. Results: Figure 1: Number of task repetitions 90 80 70 60 50 40 30 Baseline 1 2 3 4 5 6 7 Day Answer the following questions. Up to three people may contribute. 1. (2 points) You start with this experimental hypothesis: After seven days of consuming MaxTreme Wonder Liquid, subjects will show greater endurance (measured as a significant increase in number of repetitions) compared to pre-consumption levels. a. What is the null hypothesis? b. Taken without criticism, do these data support the experimental hypothesis? 2. (1 points) What is the dependent variable for this experiment? 3. (2 points) Name at least two controlled variables. 4. (2 points) The hypothesis assumes that the changes in the independent variable were the only things which could affect the dependent variable. In this case, that's a bad assumption; there is something else which could explain the change in the dependent variable. What is it? 5. (3 points) The company listens to your analysis and wants you to redesign the experiment to fix the problems you have identified. Explain how you would change the experimental method to avoid the issue you identified in question 4.
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For the first seven questions, refer to the description below: In an experiment, a scientist was testing the hypothesis that subjects' ability to hear faint sounds will improve the more time they spend unable to see. She made subjects wear a set of goggles which completely blocked vision for two weeks. During this time, she had them take daily hearing tests, in which the subjects had to respond to sounds of varying intensity. On each day, she recorded the lowest volume which subjects could reliably hear. 1. What are the independent and dependent variables for this experiment? Lowest volume subject could hear How long the subject was wearing goggles 2. Choose the best option to complete the following statement of the null hypothesis for this experiment: "The minimum sound volume that subjects respond to will ["increase", "decrease", "not change"] with more time spent wearing the goggles." 3. When should the scientist decide what analysis method to use with her data? a. Before she begins the experiment b. Once she gets data from the first subject c. Once she finishes getting data from all the subjects d. Once she has looked at the data and can determine which analysis method would show that her hypothesis is supported 4. Which of these would be a reasonable variable to control in this experiment? (Choose all correct answers) a. The zodiacal signs (e.g. Aquarius, Leo, Pisces) of the subject b. The subject's previous exposure to loud sounds c. How well the subject can see before putting on the goggles 5. The scientist measures sound sensitivity daily with ten subjects, each of whom wears the goggles for fourteen days. What statistical test should she use to determine whether the average minimum volume detected from the ten subjects on day 1 is significantly different from the average minimum volume detected by the same subjects on day 14? a. R-squared b. Unpaired t test c. Paired t test 6. When she performs the test to compare day 1 to day 14, she gets a p-value of 0.075. What does that mean? a. There is a 7.5% chance that the null hypothesis is true b. There is a 7.5% chance that the averages on day 1 and day 14 are really different c. There is a 7.5% chance that the subjects cheated in the experiment d. The minimum volume that the subjects could detect was 7.5% lower on day 14 than on day 1 7. If the scientist wanted to use a control group in this experiment, which of these would be the best way to do so? a. Have the same subjects repeat the experiment, and see if it comes out the same way b. Have a different group of subjects do the experiment exactly the same way c. Have a different group of subjects do the experiment, but have them wear headgear which blocks their hearing and test their ability to see faint light d. Have another group of subjects do the experiment, but without the goggles, and test their ability to hear faint sounds
Dominador T.
(a) An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The new bulb had a lifetime of 1200.2 hours, using a sample of 40,000 bulbs. Although the difference is quite small, the effect was statistically significant. The explanation is A. that the sample size is very large. B. that the mean of 1200 is large. C. that new designs typically have more variability than standard designs. D. all of the above. (b) Does 30 minutes of aerobic exercise each day provide significant improvement in mental performance? To investigate this issue, a researcher conducted a study with 150 adult subjects who performed aerobic exercise each day for a period of six months. At the end of the study, 200 variables related to the mental performance of the subjects were measured on each subject and the means compared to known means for these variables in the population of all adults. Nine of these variables were significantly better (in the sense of statistical significance) at the α=0.05 level for the group that performed 30 minutes of aerobic exercise each day as compared to the population as a whole, and one variable was significantly better at the α=0.01 level for the group that performed 30 minutes of aerobic exercise each day as compared to the population as a whole. It would be correct to conclude A. that there is very good statistical evidence that 30 minutes of aerobic exercise each day provides some improvement in mental performance. B. that there is very good statistical evidence that 30 minutes of aerobic exercise each day provides improvement for the variable that was significant at the α=0.01 level. We should be somewhat cautious about making claims for the variables that were significant at the α=0.05 level. C. that these results would have provided very good statistical evidence that 30 minutes of aerobic exercise each day provides some improvement in mental performance if the number of subjects had been larger. It is premature to draw statistical conclusions from studies in which the number of subjects is less than the number of variables measured. D. none of the above. (c) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) μ and standard deviation σ=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but you believe that the mean nicotine content is actually higher than advertised. To explore this, you test the hypotheses H0:μ=1.5, Ha:μ>1.5 and you obtain a P-value of 0.052. Which of the following is true? A. You have failed to obtain any evidence for Ha. B. This should be viewed as a pilot study and the data suggests that further investigation of the hypotheses will not be fruitful at the α=0.05 significance level. C. At the α=0.05 significance level, you have proven that H0 is true. D. There is some evidence against H0, and a study using a larger sample size may be worthwhile.
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