Week 4 - Bobby Illig 7.22 Using the z table in Appendix B,...

Bobby Illig
7.22 Using the z table in Appendix B, calculate the following percentages for a z score of 2 0.08:
a. Above this z score
b. Below this z score
c. At least as extreme as this z score
a. Above this z score P (z > –0.08) = 0.5319
b. Below this z score P (z < –0.08) = 0.4681
c. At least as extreme as this z score P (z ≥ 0.08) + P (z ≤ –0.08) = 2 x 0.4681 = 0.9362
7.32 If the cutoffs for a z test are –2.58 and 2.58, determine whether you would reject or fail to reject the
null hypothesis in each of the following cases:
a. z 5 2 0.94
b. z 5 2.12
c. A z score for which 49.6% of the data fall between z and the mean
c. A z score for which 49.6% of the data fall between z and the mean Here the z score is, z = 2.65 Since
z = 2.65 > 2.58, we have to reject the null hypothesis.
7.36 Assume that the following set of data represents the responses of 10 participants to three similar
statements. The participants rated their agreement with each statement on a scale from 1 to 7.
a. There is a piece of dirty data in this data set. Identify it and explain why it is dirty.
b. Assume that you have decided to throw out the piece of dirty data you identified in part (a) and
replace it with the mean for that variable. What is the new data point?
c. Assume that you have decided to throw out the piece of dirty data you identified in part (a) and re-
place it with the mean of that participant’s responses. What is the new data point?
7.40 Height and the z statistic: Imagine a class of thirty-three 15-year-old girls with an average height of
62.6 inches. Remember, m 5 63.8 inches and s 5 2.66 inches.
a. Calculate the z statistic.
b. How does this sample of girls compare to the distribution of sample means?
c. What is the percentile rank for this sample?