Question

Consider the following hypothesis test:

H0 : u >= 20

Ha : u < 20

A sample of 45 provided a sample mean of 19.6. The population standard deviation is 2.

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 a=.05 can it be concluded that the population mean is less than 20?

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

State the rejection rule: Reject  if  is - Select your answer -greater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 5 the critical value.

Using a=.05, can it be concluded that the population mean is less than 20?

Answer 1

Answer)

As the population s.d is known here we can use standard normal z table here to conduct the test

Null hypothesis Ho : u >= 20

Alternate hypothesis Ha : u < 20

A)

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (19.6 - 20)/(2/√45) = -1.34

B)

From z table, P(z<-1.34) = 0.0901

C)

As p-value is greater than 0.05 (given significance)

We fail to reject the null

So, we do not have enough evidence to conclude that, u is less than 20

D)

From z table, P(z<-1.645) = 0.05

So, critical value is -1.645

Rejection region is

Reject Ho if test statistics is less than -1.645

As -1.34 is not less than -1.645

We fail to reject Ho

So, we do not have enough evidence to conclude that, u is less than 20