Question

≈ 17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is = 18. Let be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that has a normal distribution and = 4.2. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? : = 18; :   < 18; left-tailed : ≠ 18; :   = 18; two-tailed      : = 18; :   > 18; right-tailed : = 18; :   ≠ 18; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume that has a normal distribution with known .The Student's , since is large with unknown .     The Student's , since we assume that has a normal distribution with known .The standard normal, since we assume that has a normal distribution with unknown . What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find (or estimate) the -value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the -value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?