Consider the following hypothesis test: H0: 27 Ha: 27 A sample of 40 provided a

Question

Consider the following hypothesis test:

H0: 27
Ha: 27

A sample of 40 provided a sample mean of 28.4. The population standard deviation is 5.

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

b. What is the p-value (to 4 decimals)? Use the value of the test statistic rounded to 2 decimal places in your calculations.

c. At = .01, what is your conclusion?

p-value is Selectgreater than or equal to 0.01, rejectgreater than 0.01, do not rejectless than or equal to 0.01, do not rejectless than 0.01, rejectequal to 0.01, do not rejectnot equal to 0.01, do not rejectItem 3 H0

d. What is the rejection rule using the critical value?

Reject H0 if z is Selectgreater than or equal to 2.33greater than 2.33less than or equal to 2.33less than 2.33equal to 2.33not equal to 2.33Item 4

What is your conclusion?
Select1.77 is greater than or equal to 2.33, do not reject1.77 is greater than 2.33, do not reject1.77 is less than or equal to 2.33, reject1.77 is less than 2.33, do not reject1.77 is equal to 2.33, reject1.77 is not equal to 2.33, do not rejectItem 5 H0

Explanation / Answer

The value of the test statistic is

Z = (X-Mean)/(SD/sqrt(N))

(28.4-27)/(5/sqrt(40)) = 1.77

b)

The p value is

P ( Z>1.77 )=1P ( Z<1.77 )=10.9616=0.0384

c)

at alpha = 0.01, we fail to reject the null hypothesis as the p value is 0.0384 which is not less than 0.01

d)

The rejection rule is if the if the z stat is greater than z critical then we reject the null hypothesis . for alpha =0.01 , the critical value is 2.33

do not reject 1.77 is less than or equal to 2.33

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