Let x be a random variable representing dividend yleld of bank stocks. We may assume that x has a normal distribution with a = 3.1%. 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 vield 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? State the null and alternate hypotheses. Will you use a left-tailed, right-tailled, or two-taled test? O Ho: H = 4.7%; H: u < 4.7%; left-tailed O Ho: H > 4.7%; H1: µ = 4.7%; right-tailed O Ho: H = 4.7%; H;: µ > 4.7%; right-tailed O Ho: H = 4.7%; H: H* 4.7%; two-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 n is large with unknown o. The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since we assume that x has a normal distribution with known a. 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.)
Let x be a random variable representing dividend yleld of bank stocks. We may assume that x has a normal distribution with a = 3.1%. 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 vield 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? State the null and alternate hypotheses. Will you use a left-tailed, right-tailled, or two-taled test? O Ho: H = 4.7%; H: u < 4.7%; left-tailed O Ho: H > 4.7%; H1: µ = 4.7%; right-tailed O Ho: H = 4.7%; H;: µ > 4.7%; right-tailed O Ho: H = 4.7%; H: H* 4.7%; two-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 n is large with unknown o. The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since we assume that x has a normal distribution with known a. 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.)
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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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 = 3.1%. 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 yleld isu = 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?
State the null and alternate hypotheses. Will you use a left-tailed, right-talled, or two-tailed test?
O Ho: H = 4.7%, H1: H < 4.7%; left-tailed
O Ho: H > 4.7%; H1: H = 4.7%; right-tailed
O Ho: H = 4.7%; H1: H > 4.7%; right-tailed
O Ho: H = 4.7%; H1: µ # 4.7%; two-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, sincen is large with unknown o.
O The standard normal, since we assume that x has a normal distribution with unknown o.
O The Student's t, since we assume that x has a normal distribution with known o.
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.)
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