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...
icon
Related questions
Question

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.    
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON