Consider the following hypothesis test: H0: 50 Ha: > 50 A sample of 60 is used a

Question

Consider the following hypothesis test: H0: 50 Ha: > 50 A sample of 60 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 x = 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?

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

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

c. With x = 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?

Explanation / Answer

here as sample size is higher we will use zstat.

std error of mean =std deviation/(n)1/2 =0.7746

and for 0.05 level and one tail test z critical =1.6445

a) for x=52,5

test stat z=(X-mean)/std error =(52.5-50)/0.7746 =3.227

as zstat is higher then critical value ; it can be concluded that population mean is greater then 50

b) for x=51

test stat z=(X-mean)/std error =(51-50)/0.7746 =1.291

as zstat is lower then critical value ; it can not be concluded that population mean is greater then 50

c) for x=51.8

test stat z=(X-mean)/std error =(51.8-50)/0.7746 =2.324

as zstat is higher then critical value ; it can be concluded that population mean is greater then 50

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