STAT 200 Introduction to Statistics - QUIZ 3 (2175) Dr. Cindy McCullagh 1. A single sample with a mean of 24.8 and s = 5.1 consists of 20 measurements. Find the values for t that correspond to a) the top 5% of the distribution b) the middle 95% of the distribution 2. Two samples were compared in an independent measures study. The larger sample (n = 21) had a variance of 34 and the smaller sample (n = 13) had a variance of 40. a) Determine the pooled variance for these samples. b) Calculate the estimated standard error for the mean difference. 3. Which is greater? Explain. a) The z-value that cuts off the top 1% of a distribution -OR- the t-value that cuts off the top 1% of a distribution? b) The standard deviation of a sample -OR- the standard error of the mean? 4. When conducting a hypothesis test, under which conditions are you more likely to reject the null hypothesis? Assume other conditions remain the same. Explain your answers for each of the four scenarios below. STAT 200 Introduction to Statistics - QUIZ 3 (2175) Dr. Cindy McCullagh a) = 0.01 or = 0.05 b) A one-tailed test or a two-tailed test c) Sample standard deviation is 1 or 10 d) Sample size is 20 or 50 Questions 5-7 are worth 20 points each. For problems involving hypothesis testing, be sure to include the following: Ho , H a, the random variable and what it represents, the test statistic (including all calculations), EITHER the p-value or the critical value (which will be used to make your decision), and your answer to the question that was asked. Be sure to clearly state your decision (\"reject\" or \"fail to reject\" the null hypothesis in terms of the question asked) and your reason for making this decision. 5. A researcher wants to determine whether waking up an hour earlier after going off daylight savings time (essentially, getting up when you would have BEFORE the time change) improves student test scores during the fall semester. For a given test, scores are normally distributed with a population mean of 50 and = 14. a) If a sample of 28 students who wake up an hour earlier has a mean of 55.5, can the researcher conclude that this condition results in significantly better scores? Use a one-tailed test with = 0.05. b) Calculate Cohen's d and interpret your result. 6. Researchers hypothesize that pulling an \"all-nighter\" will significantly reduce student test scores. Fifteen students were selected to complete a test at 11:00 am on the first day and again at 11:00 am on the second day without sleeping in between tests. The results are shown below. STAT 200 Introduction to Statistics - QUIZ 3 (2175) Dr. Cindy McCullagh day 1 day 2 14 12 10 11 12 10 9 8 8 5 5 6 9 10 7 8 11 9 12 10 10 7 14 13 8 8 6 4 9 9 a) Do the data indicate a significant reduction in test scores with = 0.05? b) Sketch a graph showing this result and the reason for your decision. 7. When conducting a marketing survey, a research team finds that 428 out of 951 people are willing to respond to a 5-question survey and that 398 out of 980 are willing to respond to a 15-question survey. At a 0.05 significance level, does the length of the survey significantly change how many people are willing to respond