Question

Researchers wish to test the efficacy of a program intended to reduce the length of labor in childbirth. The accepted mean labor time in the birth of a first child is 15.3 hours. The mean length of the labors of 13 first-time mothers in a pilot program was 10.8 hours with a standard deviation of 3.1 hours. Assuming a normal distribution of times of labor, test at the 10% level of significance whether the mean labor time for all women following this program is less than 15.3 hours.

State the null and alternative hypotheses: Ho: H1: This is a _________ test and the claim is the_________.For this study, we should use a_________.The p-value is:_________(round to four decimal places). Because P_________0.10 we_________the null hypothesis. Thus,_________.

Answer 1

The Hypotheses are:

This test is a left tailed T-test since the population standard deviation is missing and sample size is less than 30, but the distribution is approximately normal so,
Rejection region:

Reject Ho if T < -t _{0.1, 12} =-1.36

Test statisic:

The P-value computed using excel too at calculated T score and degree of freedom as

P-value= 0.0001

Conclusion:

Since the P-value is less than 0.10 hence we reject the null hypothesis and conclude that there is enough evidence to support the claim.