Consider the following hypothesis test: H0: = 15 Ha: 15 A sample of 50 provided

Question

Consider the following hypothesis test:

H0: = 15

Ha: 15

A sample of 50 provided a sample mean of 14.17. The population standard deviation is 3.

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

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

c. Using = .05, can it be concluded that the population mean is not equal to 15? SelectYesNoItem 3

Answer the next three questions using the critical value approach.

d. Using = .05, what are the critical values for the test statistic? (+ or -)

e. State the rejection rule: Reject H0 if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 5 the lower critical value and is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 6 the upper critical value.

f. Can it be concluded that the population mean is not equal to 15?
SelectYesNoItem 7

Explanation / Answer

Given that

A sample of 50 provided a sample mean of 14.17. The population standard deviation is 3.

so we calculate the t stat as

T = (X-Mean)/(SD/sqrt(n)) = (15-14.17)/(3/sqrt(50)) = 1.956

nopw lets calculate the critical value for degree of freedom = n-1 = 50-1 = 49 for alpha = 0.05 , which is 2.009

as t stat is less than the t critical hence we fail to reject the null hypothesis and conclude that H0: = 15

p value approach

is to find the p value of the test statistic from the t table and then compare it with the alpha 0.05 , if the p value is less than 0.05 then we can reject the null hypothesis , else not

as can be seen from the t table the p value is 0.0561, again we fail to reject the null hypothesis .

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