Question

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

Consider the following hypothesis test.

H₀: μ ≥ 20

H_a: μ < 20

A sample of 50 provided a sample mean of 19.1. The population standard deviation is 2.

(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)

Using

α = 0.05,

state your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ < 20.Reject H₀. There is insufficient evidence to conclude that μ < 20.     Do not reject H₀. There is sufficient evidence to conclude that μ < 20.Do not reject H₀. There is insufficient evidence to conclude that μ < 20.

(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 < 20.Reject H₀. There is insufficient evidence to conclude that μ < 20.     Do not reject H₀. There is sufficient evidence to conclude that μ < 20.Do not reject H₀. There is insufficient evidence to conclude that μ < 20.

Answer 1

Solution :

= 20

= 19.1

= 2

n = 50

This is the left tailed test .

The null and alternative hypothesis is

H0 :   ≥ 20

Ha : < 20

a) Test statistic = z

= ( - ) / / n

= (19.1 - 20) / 2 / 50

= -3.18

b) P (Z < -3.18) = 0.0007

P-value = 0.0007

= 0.05  

0.0007 < 0.05

c)Reject H0. There is sufficient evidence to conclude that μ < 20.

d) = 0.05  

The left tailed critical value is -1.65

Reject H0. There is sufficient evidence to conclude that μ < 20