2. [-/20 Points] - BBBASICSTAT8ACC 9.1.019. ASK YOUR TEACHER PRACTICE ANOTHE Let x be a random variable representing dividend yield of bank stocks. We may assume that X has a normal distribution with a = 2.1%. A random sample of 10 bank stocks gave the following yields ( 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 u = 4.7%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.7%? 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, right-tailed, or two-tailed test? 0 H0: )4 = 4.7%; H1: )1 4.7%; two-tailed O H0: )1 > 4.7%; H1: )1 = 4.7%; righttailed O HO: p = 4.7%; H1: 1,: 4.7%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 0 The standard normal, 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 unknown 0. O The Student's t, since n is large with unknown (1. O The Student's t, since we assume that X has a normal distribution with known 0. Compute the 2 value of the sample test statistic. (Enter a number. Round your answer to two decimal places.) :l (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 Pvalue. (Select the correct graph.) (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 O -3 -2 -1 0 1 2 3 O -3 -2 -1 0 1 2 3 CHOICE C CHOICE D O -3 -2 2 -3 -2 -1 1 2 (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. At the a = 0.0 1 levO 3 2 1 0 l 2 3 O 3 2 1 O 1 2 3 CHOICE C CHoxcE D (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signicant at level a? 0 At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. 0 At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. 0 At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. 0 At the 11 = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. 0 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. 0 There is insufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market. Need Help