In 1995?, a reproductive clinic reported 43 live births to 168 women under the age of? 38, but only 6 live births for 80 clients aged 38 and older. Is there evidence of a difference in the effectiveness of the? clinic's methods for older? women?

?a) Test an appropriate hypothesis and state your conclusion.? (Use the pooled sample proportion when checking the? success/failure condition.)

?b) If you concluded there was a? difference, estimate that difference with a 95?% confidence interval and interpret your interval in context.

1.) Let p₁ be the proportion of live births for clients under the age of 38 and p₂ be the proportion of live births for clients aged 38 and older. Choose the correct null and alternative hypotheses below.

A. H₀: p₁-p₂≠0

HA: p₁-p₂=0

B. H₀: p₁-p₂=0

HA: p₁-p₂<0

C. H₀: p₁-p₂≠0

HA: p₁-p₂>0

D. H₀: p₁-p₂=0

HA: p₁-p₂≠0

2.) Determine the test statistic.

z= ____ (Round to two decimal places as needed.)

3.) Find the P-value.

P=____ (Round to four decimal places as needed.)

4.) What is the result of this hypothesis test at a level of significance of 0.05?

A. Reject the null hypothesis because there is not sufficient evidence to support the claim that there is a difference in the effectiveness of the methods.

B. Do not reject the null hypothesis because there is not sufficient evidence to support the claim that there is a difference in the effectiveness of the methods.

C. Reject the null hypothesis because there is sufficient evidence to support the claim that there is a difference in the effectiveness of the methods.

D. Do not reject the null hypothesis because there is sufficient evidence to support the claim that there is a difference in the effectiveness of the methods.

5.) If you concluded there was a difference, estimate that difference, p₁-p₂, with a 95% confidence interval. Select the correct answer below and, if necessary, fill in the answer boxes within your choice.

A.The confidence interval is (__,__) (Round to three decimal places as needed.)

B.There was no difference in the effectiveness of the methods.

6.) Now, Interpret your interval, if any was created. Select the correct answer below and, if necessary, fill in the answer boxes within your choice.

A. There is 95% confidence that the proportion of successful live births at the clinic is between __% and __% higher for mothers under 38 than for those 38 and older. (Round to one decimal place as needed.)

B. There was no difference in the effectiveness of the methods.