Question

Consider the following hypothesis test:

H0: ≤ 26

Ha: > 26

A sample of 40 provided a sample mean of 27.4. The population standard deviation is 5.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 4 decimals)?

c. At = .01, what is your conclusion? p-value is H0

d. What is the rejection rule using the critical value?

Reject H0 if z is

What is your conclusion?

Answer 1

H0: <= 26

Ha: > 26

a)

test statistics

z = - / / sqrt(n)  

= 27.4 - 26 / 5 / sqrt(40)

= 1.77

b)

p-value = P( Z > z)

= P( Z > 1.77)

= 1 - P( Z < 1.77)

= 1 - 0.9616

= 0.0384

c)

Since p-value > 0.01 significace level, we do not have sufficient evidence to reject H0.

That is , we fail to reject H0.

d)

Critical value at 0.01 significance level is 2.326

Decision rule - Reject H0 if test statistics z > 2.326

Since test statistics value < 2.326, we do not have sufficient evidence to reject H0.