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 = 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 (enter a number)

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. The standard normal, since we assume that x has a normal distribution with known σ. The Student's t, since we assume that x has a normal distribution with known σ.

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.)

Answer 1

To Test :-

H0 :- µ = 4.8
H1 :- µ > 4.8

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 5.38 - 4.8 ) / ( 3.1 / √( 10 ))
Z = 0.5917

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Critical value Z(α) = Z(0.01) = 2.326
Z < Z(α) = 0.5917 < 2.326
Result :- Fail to reject null hypothesis

Decision based on P value
Reject null hypothesis if P value < α = 0.01 level of significance
P value = P ( Z < 0.5917 )
P value = 0.2770
Since 0.277 > 0.01 ,hence we fail to reject null hypothesis
Result :- We fail to reject null hypothesis

Part a)

α = 0.01

Part b)

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

Part c)

Z = 0.59

Part d)

P value = 0.2770