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 null hypothesis is true?
b. What is the probability that you will make a Type I error given that the null hypothesis is false?

7. Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data.

a    b    c
4    6    7
3    7    8
2    8    5
1    4    7
4    6    9
2    4    2
a.    Compute L for each subject using the contrast weights -1, 0, and 1.
That is, 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 each subject) you created.

13. You are conducting a study to see if students do better when they study all at once or in intervals. One group of 12 participants took a test after studying for one hour continuously. The other group of 12 participants took a test after studying for three twenty minute sessions. The first group had a mean score of 75 and a variance of 120. The second group had a mean score of 86 and a variance of 100.

a. What is the calculated t value? Are the mean test scores of these two groups 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?
4. Rank order the following in terms of power.
 

65. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.

The null and alternative hypotheses are:
a. Ho: x ¯ = 4.5, Ha : x ¯ > 4.5
b. Ho: μ ≥ 4.5, Ha: μ < 4.5
c. Ho: μ = 4.75, Ha: μ > 4.75
d. Ho: μ = 4.5, Ha: μ > 4.5
71. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:
a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher
b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same
c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher
d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher?
77. An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate 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 a sample standard deviation of 1.2. Do the data support your claim at the 1% level?

80. Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched. For some reason that she can't quite figure out, most people don't believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Now, what do you think?

120. A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She takes four new students. She records their 18-hole scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as follows:
    Player 1    Player 2    Player 3    Player 4
Mean score before class               
Mean score after class               
The correct decision is:
a. Reject H0.
b. Do not reject the H0.

1st Discussion: In the North American court system, a defendant is assumed innocent until proven guilty.  In an ideal world, we would expect that the truly innocent will always go free, whereas the truly guilty ones will always be convicted.  Now, let us tackle the following questions?
1.    In the context of the Type I error and Type II error, can you relate a court trial scenario in terms of these two errors?
2.    What would be your ideal situation if you are the defendant?
3.    What would be your ideal situation if you are the prosecuting attorney?
4.    Lastly, what do you think of the scenario of an ideal world where we expect that no innocent will be found guilty and all guilty will be convicted in the context of Type I error and Type II error?

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