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 CO2 produced to O2 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 "women 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- 97. 100- 934 91+ 96 960 1019 95+ t 98 92+ 95-Question 8 (2 points) In order to compare two kinds of feed, thirteen pigs are split into two groups, and each group received one feed. The following are the gains in weight (kilograms) after a fixed period of time: Feed A : 8.0 7.4 5.8 6.2 8.8 9 .5 Feed B: 12.0 18.2 8.0 9.6 8.2 9.9 10.3 We wish to test the hypothesis that Feed B gives rise to larger weight gains. The output from JMP is as follows: Difference t-Test DF Prob > It| Estimate -3.26905 ** hidden 11 0.0566 Std Error 1.53464 Lower 95% -6.64677 Upper 95% 0.10868 Assuming equal variances The p-value for the test is: O.0566 O .0283 .1132 O 2.130Question 9 (2 points) Which of the following conditions doesn't need to be met before you can use a two- sample procedure? O The responses in each group are independent of each other. Each group is considered to be a sample from a distinct population. The same variable is measured in both samples. The goal is to compare the means of the two groups. Data in two samples are matched together in pairs that are compared. Question 10 (2 points) The Tribune claims that the time of travel from downtown to the University via the bus has an average of u = 27 minutes. A student who normally takes this bus believes that u is greater than 27 minutes. A sample of six ride times taken to test the hypothesis of interest gave a mean of 27.5 minutes and standard deviation of 2.43 minutes. The value of the test statistic for testing this hypothesis is - 0.532 0.460 0.504 -0.460 -0.504RER(%)+ Placeboo Caffeine- 100+ 98+ 985 97+ 100+ 93+ 91+ 96- 96- 101+ 95+ 98- 92+ 95+ 99- A. What type of analysis will be appropriate for this data? Why? (2 points)+ B. Perform the appropriate hypothesis test showing all steps. (8 points)+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)~ 47,51,54,62,44,51,48,65,42,44,71,682 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)+ + B. Perform the appropriate hypothesis test showing all steps. (8 points)+ C. Verify your conclusion in part B by building a 95% confidence interval for the difference of the means. (4 points)+Question 1 (2 points) Which of the following statements are correct? 1. The t distribution has more area in its tails than the z distribution for all nITI Unequal -2.4048 7.9 0.0431 Equal 2.2596 11.0 0.0451 For Hy: Variances are equal, F' = 6.85 DF = (6,5) Prob>F' = 0. 0520 The appropriate test statistic and p-value are : Ot=-2.4048; p-value = .0431 Ot =-2.4048; p-value = .0216 Ot = -2.2596; p-value = .0451 Ot=-2.2596; p-value = .0256Question 7 (2 points) Which of the following statements is false? 1. We use one-sample procedures when our samples are equal in size but aren't independent. Il. Everything else being equal, a confidence interval based on 15 degrees of freedom will be narrower than one based on 10 degrees of freedom. Ill. The samples used in all two-sample procedures must be of the same size. I only ll only OilI only I and Ill only None of the above gives the correct response