Question

Consider the following hypothesis test:

H0: n greater than or equal to 20

Ha: n less than 20

a sample of 45 provided a sample mean of 19.6. 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? (3 decimals)

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

________

State the rejection rule. Reject H0 if z is __________ the critical value.

Answer 1

Solution :

= 20

= 19.6

= 1.8

n = 45

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   ≥ 20

H_a : < 20

a) Test statistic = z

= ( - ) / / n

= (19.6 -20 ) /1.8 / 45

= -1.49

b) P (Z < -1.49 ) =0.068

P-value = 0.068

= 0.05  

The significance level is α=0.05

The critical value for a left-tailed test is z_c​= −1.645.

p= 0.068 ≥0.05, it is concluded that the null hypothesis is not rejected.

Reject H0 if z is z = -1.491 ≥ z_c = -1.64 the critical value.