Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with = 3.3%. A random sample of 10 bank stocks gave the following yields (in percents).5.74.86.04.9 4.0 3.46.5 71 5.3 6.1The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is u= 4.5%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.5%?Use a = 0.01. Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with a = 3.5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.5%. Do these data indi(a) What is the level of significance?0.01State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?O Ho: = 4.5%; H₁: μ> 4.5%; right-tailedO Ho:= 4.5%; H₁: μ ‡ 4.5%; two-tailedO Ho: > 4.5%; H₁: μ = 4.5%; right-tailedO Ho: μ = 4.5%; H₁: μ< 4.5%; left-tailed(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.O The Student's t, since n is large with unknown o.O The standard normal, since we assume that x has a normal distribution with known σ.O The Student's t, since we assume that x has a normal distribution with known σ.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. (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. Sketch the sampling distribution and show the area corresponding to the P-value.0-3-2-2-1 0-101123230-3-2 -1-2-10012230-30-3(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.O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.3(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 marketO 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 mark

Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Answered: Let x be a random variable representing…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with = 3.3%. 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 71 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is u= 4.5%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.5%?Use a = 0.01.

Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with a = 3.
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 = 4.5%. Do these data indi
(a) What is the level of significance?
0.01
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
O Ho: = 4.5%; H₁: μ> 4.5%; right-tailed
O Ho:
= 4.5%; H₁: μ ‡ 4.5%; two-tailed
O Ho: > 4.5%; H₁: μ = 4.5%; right-tailed
O Ho: μ = 4.5%; H₁: μ< 4.5%; left-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The Student's t, since n is large with unknown o.
O The standard normal, since we assume that x has a normal distribution with known σ.
O The Student's t, since we assume that x has a normal distribution with known σ.
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. (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.

Sketch the sampling distribution and show the area corresponding to the P-value.
0-3
-2
-2
-1 0
-1
0
1
1
2
3
2
3
0-3
-2 -1
-2
-1
0
0
1
2
2
3
0-3
0-3
(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.
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
3
(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
O 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 mark

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution