Question

Consider the following hypothesis test:

H ₀:   50

H _a:  > 50

A sample of 65 is used and the population standard deviation is 7. 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?
SelectYesNoItem 6

Answer 1

This is right tailed test.

From Z table, critical value at 0.05 significance level = 1.645

a )

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 52.5 - 50) / ( 7 / sqrt(65 ) )

= 2.88

Since test statistics > 1.645 , Reject H0.

Yes, it can be conlcude that population mean is greater than 50

b)

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 51 - 50) / ( 7 / sqrt(65 ) )

= 1.15

Since test statistics < 1.645 , Fail to reject H0.

No, it can not be conlcude that population mean is greater than 50

c)

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 51.8 - 50) / ( 7 / sqrt(65 ) )

= 2.07

Since test statistics > 1.645 , Reject H0.

Yes, it can be conlcude that population mean is greater than 50