Question

You may need to use the appropriate appendix table or technology to answer this question.

Consider the following hypothesis test.

H0: μ = 15

Ha: μ ≠ 15

A sample of 50 provided a sample mean of 14.05. The population standard deviation 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.)

p-value =

(c)

At

α = 0.05,

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 μ ≠ 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.)

test statistic≤test statistic≥

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

Answer 1

Solution:

a)

The test statistic z is given by

z =

= (14.05 - 15) / (3/50)

= -0.40

The value of the statistic z = -2.24

b)

Now , observe that ,there is   sign in H_a. So , the test is two tailed.

p value = P(Z < -2.24) + P(Z > +2.24) = 0.0125 + 0.0125 = 0025

p value = 0.0250

c)

p value is less than α = 0.05.

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

d)

α = 0.05,

α/2 = 0.025

there are two critical values.     

i.e.   1.96(Use z table to find this value)

Critical values are -1.96 and 1.96

test statistic ≤ -1.96 , test statistic ≥ 1.96

e)

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