Question

Instructions: Round all your math steps to two decimal places just like I have been doing in class.

Consider the following hypothesis test:

H₀: µ ≥ 20

H_a: µ < 20

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

a. Compute the value of the test statistic (Round to two decimal places). Answer

b. What is the p-value? (Round to four decimal places). Answer

c. Using α=0.05, what is your conclusion? Answer choices (Reject the null hypothesis.) or (Do not reject the null hypothesis)

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 20

H_a : < 20

= 19.4

= 20

= 2

n = 50

Test statistic = z

= ( - ) / / n

= (19.4 - 20) / 2 / 50

= -2.12

Test statistic = -2.12

P(z < -2.12) = 0.017

P-value = 0.017

= 0.05

P-value <

Reject the null hypothesis .