Question

Consider the following hypothesis test.

H₀: μ ≤ 25

H_a: μ > 25

A sample of 40 provided a sample mean of 26.2. The population standard deviation is 6.

(a) Find the value of the test statistic. (Round your answer to two decimal places.)

(b)Find the p-value. (Round your answer to four decimal places.)

(c)At α = 0.01, state your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ > 25.

Reject H₀. There is insufficient evidence to conclude that μ > 25.      

Do not reject H₀. There is sufficient evidence to conclude that μ > 25.

Do not reject H₀. There is insufficient evidence to conclude that μ > 25.

(d) State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic ≤

test statistic ≥

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ > 25.

Reject H₀. There is insufficient evidence to conclude that μ > 25.      

Do not reject H₀. There is sufficient evidence to conclude that μ > 25.

Do not reject H₀. There is insufficient evidence to conclude that μ > 25.

Answer 1

a)

Test statistics

z = ( - ) / ( / sqrt(n) )

= (26.2 - 25) / (6 / sqrt(40) )

= 1.26

b)

p-value = P(Z > z)

= P(Z > 1.26)

= 0.1038

c)

Since p-value > 0.01 level, Fail to reject H0.

Do not reject H₀. There is insufficient evidence to conclude that > 25.

d)

z critical value at 001 level = 2.33

Rejection rule = Reject H0 if test statistics 2.33

Conclusion - Do not reject H₀. There is insufficient evidence to conclude that > 25.