Question

 You may need to use the appropriate appendix table or technology to answer this question. Consider the following hypothesis test.

 H₀: μ = 15

 H_a: μ ≠ 15

 A sample of 50 provided a sample mean of 14.09. The population standard devlation is 3.

 (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 a = 0.05, state your conclusion.

 Reject  H₀. There is sufficient evidence to conclude that μ ≠ 15.

 OReject  H₀. There is insufficient evidence to conclude that μ ≠ 15.

 Do not reject H₀. There is sufficient evidence to conclude that ≠ 15.

 Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 15.

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

 State your conclusion.

 Reject H₀. There is sufficient evidence to conclude that μ ≠ 15. 

 Reject H₀. There is Insufficient evidence to conclude that μ ≠ 15. 

 Do not reject H₀. There is sufficient evidence to conclude that ≠ 15. 

 Do not reject H₀. There is insufficient evidence to conclude that ≠ 15.

Answer 1

Given that, sample size ( n ) = 50

sample mean = 14.09

population standard deviation = 3

The null and alternative hypotheses are,

a) Test statistic is,

b) p-value = 2 * P(Z < -2.14) = 2 * 0.0162 = 0.0324

=> p-value = 0.0324

c) Since, p-value = 0.0324 <

=> Reject H₀. There is sufficient evidence to conclude that

d) critical values at are, z^* = ± 1.96

Rejection rule is,

test statistic -1.96

test statistic 1.96

Since, test statistic = -2.14 < -1.96

=> Reject H₀. There is sufficient evidence to conclude that