In this lab assignment an experiment on caffeine dependency was conducted on a group of volunteers by some medical resea

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In this lab assignment an experiment on caffeine dependency was conducted on a group of volunteers by some medical research surot The researchers recruited 70 volunteers who drink at least 3 cups of coffee each day and are in good health. Of these 70 volunteers. So were diagnosed as a dependent based on some general substance dependence criteria. Of the 50 subjects who were diagnosed as caffeine dependent, 30 agreed to participate in a study evaluate their caffeine dependency. Before the experiment was conducted, daily caffeine intake measurements for each subject were obtained based on food diaries of the participants The experiment was conducted on two 2-day periods which occurred exactly one week apart. During one of the 2-day periods, the subjects were given a set of capsules containing the amount of caffeine normally ingested by the subject in one day. During the other study period, the subjects were given placebos. The order in which each subject received the two types of capsules was randomized. At the end of each 2-day study period, subjects were evaluated in three areas: depression symptoms, fatigue. and concentration. The experimenters were blinded to whether the subject was receiving the caffeine pills or the caffeine-free pills. In particular, researchers wanted to study the change in depression scores (Depr-Nd minus Depr-Caf) for smokers (Y) and non-smokers (N). The summary statistics for the two groups are provided below. Smoker Mean n Std. Dev. Std. Error Y 8 6.285 5.482 1.988 N 22 6.535 5.854 1.248 a) Is there sufficient evidence that change in depression scores is higher for smokers than non-smokers, on average? Use the summary statistics above to calculate the absolute value of the appropriate test statistic to answer the question. If you think the samples are independent, then assume equal variances and use Sp = 5.763.)
O 0.263 0 0.044 b) Refer to the previous question. What is the distribution of the test statistic under the null hypothesis? Select one: Oz-distribution OF-distribution with numerator df = 2 and denominator df = 24 O t-distribution with df = 28 O t-distribution with df = 7 O t-distribution with df = 29 C) A 95% confidence interval for the difference in the change in depression scores between the smokers and non-smokers is (-4.623,5.123). Using only this cc interval, what do you conclude?
1.248 a) Is there sufficient evidence that change in depression scores is higher for smokers than non-smokers, on average? Use the summary statistics above to calculate the absolute value of the appropriate test statistic to answer the question. If you think the samples are independent, then assume equal variances and use 5.763.) Select one: O 0.578 O 0.237 O 0.105 O 0.263 O 0.044 b) Refer to the previous question. What is the distribution of the test statistic under the null hypothesis? Select one: O z-distribution
C) A 95% confidence interval for the difference in the change in depression scores between the smokers and non-smokers is (-4.523.5.123) Using the content interval, what do you conclude? Select one: O There is insufficient evidence of a difference in the change in depression scores between the two groups, on average, at a = 0.05. O We cannot make any conclusions. O There is sufficient evidence of no difference in the change in depression scores between the two groups, on average, at a = 0.05. O There is sufficient evidence of a difference in the change in depression scores between the two groups, on average, at a = 0.05. O There is insufficient evidence of no difference in the change in depression scores between the two groups, on average, at a = 0.05. d) If the non-smokers were further separated into those who never smoked and those who used to smoke, is there sufficient evidence that average change in depressio scores differ between the three different groups? To answer this question, state the null and alternative hypotheses. Select one: O Ho: M1 = Pz Uz vs. Ha: M1 = H2 = M3 O Ho: M1 = U2 = M3 vs. Ha: U1 + H2 + H3
d) If the non-smokers were further separated into those who never smoked and those who used to smoke, is there sufficient evidence that average change in depression scores differ between the three different groups? To answer this question, state the null and alternative hypotheses. Select one: O Hoi uz uz vs. Ha: U1 = M2 = M3 O Hout = uz = uz vs. Ha: Hy * Uz M3 O Hout = ug = uz vs. Ha: at least one of the means is different O Ho: 1 = 2 = uz vs. Ha: at least two of the means are the same O Ho: 41 = U2 = uz vs. Ha: at least two of the means are the same