Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o = 2.6%. 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 u = 4.2%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.2%? 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? Ho: u = 4.2%; H,: µ # 4.2%; two-tailed O Ho: u = 4.2%; H,: µ < 4.2%; left-tailed O Ho: u > 4.2%; H,: µ = 4.2%; right-tailed O Ho: H = 4.2%; H,: u > 4.2%; right-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 known o. O The Student's t, since we assume that x has a normal distribution with known o. O The Student's t, sincen is large with unknown o. O The standard normal, since we assume that x has a normal distribution with unknown o. Compute the z 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.)
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o = 2.6%. 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 u = 4.2%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.2%? 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? Ho: u = 4.2%; H,: µ # 4.2%; two-tailed O Ho: u = 4.2%; H,: µ < 4.2%; left-tailed O Ho: u > 4.2%; H,: µ = 4.2%; right-tailed O Ho: H = 4.2%; H,: u > 4.2%; right-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 known o. O The Student's t, since we assume that x has a normal distribution with known o. O The Student's t, sincen is large with unknown o. O The standard normal, since we assume that x has a normal distribution with unknown o. Compute the z 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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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?
b)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
Compute the z 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.)
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?
Transcribed Image Text:Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o = 2.6%. 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 u = 4.2%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.2%? 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?
Ho: u = 4.2%; H,: µ # 4.2%; two-tailed
O Ho: u = 4.2%; H,: µ < 4.2%; left-tailed
O Ho: u > 4.2%; H,: µ = 4.2%; right-tailed
O Ho: H = 4.2%; H,: u > 4.2%; right-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 known o.
O The Student's t, since we assume that x has a normal distribution with known o.
O The Student's t, sincen is large with unknown o.
O The standard normal, since we assume that x has a normal distribution with unknown o.
Compute the z 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.)
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