Let be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with

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Let Be A Random Variable Representing Dividend Yield Of Bank Stocks We May Assume That X Has A Normal Distribution With 1 (107.82 KiB) Viewed 11 times

Let be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with = 2.9%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x - 5.38%. Suppose that for the entire stock market, the mean dividend yield is = 4.6%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.6% 7 Use a = 0.01. (a) What is the level of significance? (Enter a number.) State the null and alternate hypotheses. Will you use a left-tailed, night-tailed, or two-tailed test? H₂H-4.6%; H₂: 4.6%; two-tailed OH₂=4.6%; H₂: < 4.6%; left-tailed OH₂R>4.6%; H₁: = 4.6%; right-tailed OH: 4.6%; H₂:> 4.6%; night-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since n is large with unknown d. O The Student's t, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with known a. Compute the value of the sample test statistic. (Enter a number. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Enter a number. Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. (Select the correct graph.) CHOICE A CHOICE B -2 -1 0 1 3 -1 0 1 2 O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 3 CHOICE C (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 a? O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. O There is sufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market. CHOICE D n -2 -1 0 1 2 5:09 PM