x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.7%. 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 μ = 4.8%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.8%? Use α = 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? H0: μ = 4.8%; H1: μ < 4.8%; left-tailedH0: μ > 4.8%; H1: μ = 4.8%; right-tailed H0: μ = 4.8%; H1: μ > 4.8%; right-tailedH0: μ = 4.8%; H1: μ ≠ 4.8%; 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 x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ. The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown σ. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) 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 α? At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 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. 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.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.

x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.7%. 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 μ = 4.8%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.8%? Use α = 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? H0: μ = 4.8%; H1: μ < 4.8%; left-tailedH0: μ > 4.8%; H1: μ = 4.8%; right-tailed H0: μ = 4.8%; H1: μ > 4.8%; right-tailedH0: μ = 4.8%; H1: μ ≠ 4.8%; 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 x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ. The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown σ. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) 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 α? At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 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. 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.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.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.8%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.8%? Use α = 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?

H₀: μ = 4.8%; H₁: μ < 4.8%; left-tailedH₀: μ > 4.8%; H₁: μ = 4.8%; right-tailed H₀: μ = 4.8%; H₁: μ > 4.8%; right-tailedH₀: μ = 4.8%; H₁: μ ≠ 4.8%; 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 x has a normal distribution with unknown σ.The Student's t, since we assume that x has a normal distribution with known σ. The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown σ.

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

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 α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 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.

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.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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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