Question

Consider the following hypothesis test:

H_{0 :} μ ≥ 20

Hα : μ < 20

A sample of 45 provided a sample mean of 19.5. The population standard deviation is 1.8.

a. Compute the value of the test statistic (to 2 decimals). Enter negative value as negative number.

b. What is the p-value (to 3 decimals)?

c. Using α=0.05, can it be concluded that the population mean is less than 20 ?

d. Using α=0.05, what is the critical value for the test statistic (to 3 decimals)? Enter negative value as negative number.

Answer 1

Given :

The hypothesis test:

H₀ : μ ≥ 20

H_a : μ < 20

Sample size, n = 45

Mean,  = 19.5

Standard deviation , = 1.8

Now,

Therefore a) The test statistic is -1.86

b) The p-value is 0.031

c) there is enough statistical evidence to conclude that the population mean is less than 20

d) The critical value for the test statistic is -1.645.