Question

Consider the following hypothesis test:

Ho: u = 15

Ha: u ≠ 15

A sample of 40 provided a sample mean of 14.17. The population standard deviation is 3. Enter negative value as negative number

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. using a=0.05, can it be concluded that the population mean is not equal to 15? (select your answer: yes/ no)

answer the next three questions using the critical value approach:

D. using a=0.05, what are the critical values for the test statistic? (+ or -) (to 2 decimals)

state the rejection rule: Reject Ho is z is (select your answer: greater than or equal to/ greater than/ less than or equal to/ less than/ equal to/ not equal to) the lower critical value and is (select your answer: greater than or equal to/ greater than/ less than or equal to/ less than/ equal to/ not equal to) the upper critical value

can it be concluded that the population mean is not equal to 15? (yes/ no)

Answer 1

We know that

Population mean in the hypothesis test, mu= 15.

Sample mean, xbar= 14.17.

Population standard deviation, sigma= 3.

Sample size, n= 40.

A.

Test statistic= (xbar-mu) / sigma / sqrt(n)

= (14.17-15) / 3/sqrt(40)

= -0.83 / 0.4743416

= - 1.749794 ~ -1.75

B.

The p-value can be found from a z-distribution table. The value is 0.04006 ~ 0.0401.

C.

The rejection region will be on the left and the right side. Thus, the critical p-value is 0.025.

Since our test statistic is greater than this value, we will fail to reject the null hypothesis. Thus, it cannot be concluded that the population mean is not equal to 15. The answer is no.

D.

The significance level is 0.05. Thus, the rejection region will be 0.025 on each side of the distribution.

Thus, the critical values (as can be seen from a standard normal distribution or a z distribution) are + or - 1.96.

No, it cannot be concluded that the population mean is not 15 since the test statistic is greater than the lower limit of the acceptable region (-1.75 > -1.96) and the test statistic is less than the upper limit of the acceptable region (-1.75<1.96).

Thus, the null hypothesis cannot be rejected.