Chapter 9.1, Problem 19P

For Problems 19-24, please provide the following information.

(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?

(b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the z value of the sample test statistic.

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-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 $\alpha$?

(e) Interpret your conclusion in the context of the application.

Dividend Yield: Australian Bank Stocks Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with $\sigma =2.4\%.$ A random sample of 10 Australian bank stocks gave the following yields:

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The sample mean is $\bar{x}=5.38\%$. For the entire Australian stock market, the mean dividend yield is $\mu =5.38\%.$ (Reference: Forbes). Do these data indicate that the dividend yield of all Australian bank stocks is higher than $4.7\%?$ Use $\alpha =0.01$.