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Auburn University *

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2010

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Statistics

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May 15, 2024

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AP Statistics 11.04 Comparing Independent Sample Means Directions: Complete the assignment. Clearly label each answer. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit. (24 points) 1. A study of the effect of caffeine on muscle metabolism used sixteen female volunteers who each underwent arm exercise tests. Eight of the women were randomly selected to take a capsule containing pure caffeine one hour before the test. The other randomly selected women received a placebo capsule. During each exercise the subject's respiratory exchange ratio (RER) was measured. (RER is the ratio of CO 2 produced to O 2 consumed and is an indicator of whether energy is being obtained from carbohydrates or fats). The question of interest to the experimenter was whether, on average, caffeine lowers RER . The two populations being compared are “women who have not taken caffeine” and “ wo men who have taken caffeine”. If caffeine has no effect on RER the two sets of data can be regarded as having come from the same population. The data: RER(%) Placebo Caffeine 100 98 98 97 100 93 95 91 96 96 101 95 98 92 95 99 A. What type of analysis will be appropriate for this data? Why? (2 points) T-test will be the most appropriate for this data bc it is comparing independent samples, the distribution is approximate normality, and the standard deviation of the population is unknown.

B. Perform the appropriate hypothesis test showing all steps. (8 points) Caffeine: Sample size: n=8 X-bar=95.125 Sx=2.90 Min=91 Max=99 Med=93.5 Q1=92.5 Q3=97.5 Placebo: Samples size: n=8 X-bar=97.875 Sx=2.36 Min=95 Max=101 Med=98 Q1=95.5 Q3=100 Conclusion: we can assume that the samples were randomly selected, that they ’re independent from each other, and that it’s approximate normality. 2. A psychologist studying the human factors of computer keyboards set up an experiment to compare two different keyboard designs. He measures the number of words per minute typed by one randomly selected group on Keyboard A and then he measures the number of words typed per minute by another randomly selected group of people on Keyboard B. Use the data below to determine if the typing speeds on the two different keyboards are significantly different. Keyboard A (words per minute) Keyboard B (words per minute) 47,51,54,62,44,51,48,65,42,44,71,68 68,39,52,33,55,58,67,62,61,49,44,49 A. What type of analysis will be appropriate for this data? Why? (2 points) T-test will be the most appropriate for this data bc it is comparing independent samples and the distribution is approximate normality B. Perform the appropriate hypothesis test showing all steps. (8 points) Keyboard A: Samples size: n=12 x-bar = 53.08 Sx = 10.89 Min = 42 Max = 71 Med = 51 Q1 = 45.5

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