http://imgur.com/Qyg8JzS ^Larger image of the question. In 2002. a reproductive

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http://imgur.com/Qyg8JzS

^Larger image of the question.

In 2002. a reproductive clinic reported 43 live births to 152 women under the age of 38. but only 6 live births for 76 clients aged 38 and older. Is there evidence of a difference in the effectiveness of the clinic's methods for older women? Test an appropriate hypothesis and state your conclusion. (Use the pooled sample proportion when checking the success/failure condition.) If you concluded there was a difference, estimate that difference with a 90% confidence interval and interpret your interval in context. Let p_1 be the proportion of live births for clients under the age of 38 and p_2 be the proportion of live births for clients aged 38 and older. Choose the correct null and alternative hypotheses below. H_O: p_1 - p_2 = 0 H_A: p_1 - p_2 notequalto 0 H_O: p_1 - p_2 notequalto 0 H_A: p_1 - p_2 = 0 H_O: p_1 - p_2 = 0 H_A: p_1 - p_2 0 Determine the test statistic z = (Round to two decimal places as needed.) Find the P-value. P = (Round to four decimal places as needed.) What is the result of this hypothesis test at a level of significance of 0.1? Reject the null hypothesis because there is sufficient evidence to support the claim that there is a difference in the effectiveness of the methods. 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. 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. 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. If you concluded there was a difference, estimate that difference. p_1 - p_2. with a 90% confidence interval. Select the correct answer below and. if necessary, fill in the answer boxes within your choice. The confidence interval is (). (Round to three decimal places as needed.) There was no difference in the effectiveness of the methods. Interpret your interval, if any was created. Select the correct answer below and, if necessary, fill in the answer boxes within your choice. There is 90% 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.) There was no difference in the effectiveness of the methods.

Explanation / Answer

option A is correct

p1=x1/n1=43/152=0.2829

and p2=x2/p2=6/76=0.0789

pooled sample proportion p=(x1+x2)/(n1+n2)=0.2149

hence std error =(p(1-p)/n)1/2=0.0272

hence test stat z=(p1-p2)/std error =7.4971

p value =0.0000

option A ) reject the null hypothesis

b) for 90% CI, z=1.6445

hence confidence interval =(p1-p2)+/- z*std error =0.1592 ; 0.2487

option A b/w 15.92% to 24.87%

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