Question

Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 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 yield is μ = 5.0%. Do these data indicate that the dividend yield of all bank stocks is higher than 5.0%? 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 = 5%; H₁: μ ≠ 5%; two-tailedH₀: μ = 5%; H₁: μ < 5%; left-tailed    H₀: μ = 5%; H₁: μ > 5%; right-tailedH₀: μ > 5%; H₁: μ = 5%; right-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

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 standard normal, since we assume that x has a normal distribution with unknown σ.The Student's t, since n is large with unknown σ.

What is the value of the standardized 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.

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.    

Answer 1

a)
Level of significance is 1%

H0: mu = 5
Ha: mu > 5
right tailed

b)
The standard normal, since we assume that x has a normal distribution with known σ

test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (5.38 - 5)/(3.1/sqrt(10))
z = 0.39

c)
p-value = 0.3483
At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

e)
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.