Question

Consider the following hypothesis test:

H 0:   50

H a:  > 50

A sample of 70 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05.

a. With  = 52.5, what is the value of the test statistic (to 2 decimals)?

Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 2

b. With  = 51, what is the value of the test statistic (to 2 decimals)?


Can it be concluded that the population mean is greater than 50?
SelectYesNoItem 4

c. With  = 51.8, what is the value of the test statistic (to 2 decimals)?

Can it be concluded that the population mean is greater than 50?
Yes No

Answer 1

Solution :

Given that,

= 50

= 6

n = 70

(a)

= 52.5

Test statistic = z

= ( - ) / / n

= (52.5 - 50) / 6 / 70

z = 3.49

This is the right tailed test .

= 0.05

Z = Z_0.05 = 1.65

Critical value = 1.65

Test statistic > crtitical value

Reject the null hypothesis .

It can be concluded that the population mean is greater than 50 .

Yes .

(b)

= 51

Test statistic = z

= ( - ) / / n

= (51 - 50) / 6 / 70

z = 1.39

This is the right tailed test .

= 0.05

Z = Z_0.05 = 1.65

Critical value = 1.65

Test statistic < crtitical value

Fail to reject the null hypothesis .

It can not be concluded that the population mean is greater than 51 .

No

(c)

= 51.8

Test statistic = z

= ( - ) / / n

= (51.8 - 50) / 6 / 70

z = 2.51

This is the right tailed test .

= 0.05

Z = Z_0.05 = 1.65

Critical value = 1.65

Test statistic > crtitical value

Reject the null hypothesis .

It can be concluded that the population mean is greater than 51.8

Yes .