Question

Consider the following hypothesis test.

H0: μ ≤ 25

Ha: μ > 25

A sample of 40 provided a sample mean of 26.8. 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.)

p-value =

(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) The value of test statistic here is computed as:

Therefore 1.90 is the test statistic value here. ( rounded to 2 decimal places )

b) As this is a one tailed test, an upper tailed test, the p-value here is computed from the standard normal tables as:

p = P(Z > 1.90) = 0.0289

Therefore 0.0289 is the required p-value here.

c) As the p-value here is 0.0289 > 0.01 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. There is insufficient evidence to conclude that μ > 25.     Do not reject H₀.

d) Using critical value approach, from standard normal tables, we have here:

P(Z < 2.326) = 0.99

Therefore 2.326 is the critical value here.

As the critical value is more than the test statistic value here, the test statistic lies outside the rejection region and we dont reject the null hypothesis here. Therefore Do not reject H₀