• On questions requiring a numerical answer, show how the answer was obtained, by attaching Excel files, and a copy of your manual calculations on words Exercise 4-72 on page 214 Consider the Minitab output shown below, which also includes a Z-value = 2.76 and a P-value = 0.006. (a) Is this a one-sided or a two-sided test? This is a two-sided test because you will look at areas above and below p=0.3. (b) Was this test conducted using the normal approximation to the binomial? Was that appropriate? The normal approximation to the binomial was used. It is appropriate because Np and N(1-p) are 95 and 155 respectively. 95 and 155 are both greater than 5 so a normal approximation can be used. (c) Can the null hypothesis be rejected at the 0.05 level? The null hypothesis would be rejected because the p-value 0.006 is less than 0.05. (d) Can the null hypothesis 𝐻0 : 𝑝 = 0.4 versus 𝐻1 : 𝑝 ≠ 0.4 be rejected at the 0.05 level? How can you do this without performing any additional calculations? No, it cannot be rejected. You can tell by looking at the 95% confidence interval. Since 0.4 is within the interval range, the p-value would still be too large to reject. (e) Construct an approximate 90% traditional CI for p. First, find the z-scores for the normal that would give you 5% to the left (outside area of confidence interval is divided evenly between the left and right side.) Excel was used to find a z-score or -1.6448536 for the lower bound. Because the interval wi ...
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