STATISTICS

18. You choose an alpha level of .01 and then analyze your data.a. What is the probability that you will make a Type I error given that the nullhypothesis is true?b. What is the probability that you will make a Type I error given that thenull hypothesis is false?20. True/false: It is easier to reject the null hypothesis if the researcher usesa smaller alpha (?) level.7. Below are data showing the results of six subjects on a memory test. Thethree scores per subject are their scores on three trials (a, b, and c) of amemory task. Are the subjects get- ting better each trial? Test the lineareffect of trial for the data.a433212b678464c785792a. Compute L for each subject using the contrast weights -1, 0, and 1. Thatis,compute (-1)(a) + (0)(b) + (1)(c) for each subject.b. Compute a one-sample t-test on this column (with the L values for eachsubject) you created.13. You are conducting a study to see if students do better when they studyall at once or in intervals. One group of 12 participants took a test afterstudying for one hour continuously. The other group of 12 participants tooka test after studying for three twenty minute sessions. The first group had amean score of 75 and a variance of 120. The second group had a meanscore of 86 and a variance of 100.a. What is the calculated t value? Are the mean test scores of these twogroups significantly different at the .05 level?b. What would the t value be if there were only 6 participants in each group?Would the scores be significant at the .05 level?65. Previously, an organization reported that teenagers spent 4.5 hours perweek, on average, on the phone. The organization thinks that, currently, themean is higher. Fifteen randomly chosen teenagers were asked how manyhours per week they spend on the phone. The sample mean was 4.75 hourswith a sample standard deviation of 2.0. Conduct a hypothesis test. The nulland alternative hypotheses are:a. Ho: x ¯ = 4.5, Ha : x ¯ > 4.5b. Ho: ? ? 4.5, Ha: ? < 4.5c. Ho: ? = 4.75, Ha: ? > 4.75d. Ho: ? = 4.5, Ha: ? > 4.571. Previously, an organization reported that teenagers spent 4.5 hours perweek, on average, on the phone. The organization thinks that, currently, themean is higher. Fifteen randomly chosen teenagers were asked how manyhours per week they spend on the phone. The sample mean was 4.75 hourswith a sample standard deviation of 2.0. Conduct a hypothesis test, the TypeI error is:a. to conclude that the current mean hours per week is higher than 4.5,when in fact, it is higherb. to conclude that the current mean hours per week is higher than 4.5,when in fact, it is the samec. to conclude that the mean hours per week currently is 4.5, when in fact, itis higherd. to conclude that the mean hours per week currently is no higher than 4.5,when in fact, it is not higher77. An article in the San Jose Mercury News stated that students in theCalifornia state university system take 4.5 years, on average, to finish theirundergraduate degrees. Suppose you believe that the mean time is longer.You conduct a survey of 49 students and obtain a sample mean of 5.1 with asample standard deviation of 1.2. Do the data support your claim at the 1%level?80. At Rachel’s 11th birthday party, eight girls were timed to see how long(in seconds) they could hold their breath in a relaxed position. After a twominute rest, they timed themselves while jumping. The girls thought thatthe mean difference between their jumping and relaxed times would bezero. Test their hypothesis.Relaxed time (seconds)26473022Relaxed time (seconds)23453729Jumping time(seconds)21402821Jumping time(seconds)2543353291. A powder diet is tested on 49 people, and a liquid diet is tested on 36different people. Of interest is whether the liquid diet yields a higher meanweight loss than the powder diet. The powder diet group had a mean weightloss of 42 pounds with a standard deviation of 12 pounds. The liquid dietgroup had a mean weight loss of 45 pounds with a standard deviation of 14pounds.120. A golf instructor is interested in determining if her new technique forimproving players’ golf scores is effective. She takes four new students. Sherecords their 18-hole scores before learning the technique and then afterhaving taken her class. She conducts a hypothesis test. The data are asfollows.Mean score beforeclassMean score after classPlayer 183Player 278Player 393Player 48780808686Bonus Question: Hypothesis Testing ???In the North American court system, a defendant is assumed innocent untilproven guilty. In an ideal world, we would expect that the truly innocent willalways go free, whereas the truly guilty ones will always be convicted. Now,let us tackle the following questions?In the context of the Type I error and Type II error, can you relate a courttrial scenario in terms of these two errors?What would be your ideal situation if you are the defendant?What would be your ideal situation if you are the prosecuting attorney?Lastly, what do you think of the scenario of an ideal world where we expectthat no innocent will be found guilty and all guilty will be convicted in thecontext of Type I error and Type II error?