Question

In 2001​, one county reported that among 3115 white women who had​ babies, 146 were multiple births. There were also 22 multiple births to 647 black women. Does this indicate any racial difference in the likelihood of multiple​ births?

​a) Test an appropriate hypothesis and state your conclusion.

​b) If your conclusion is​ incorrect, which type of error did you​ commit?

​a) Let p1 be the proportion of multiple births for white women and  p2 be the proportion of multiple births for black women. Choose the correct null and alternative hypotheses below.

A. Upper H 0 : p 1 minus p 2 equals 0 Upper H Subscript Upper A Baseline : p 1 minus p 2 greater than 0

B. Upper H 0 : p 1 minus p 2 equals 0 Upper H Subscript Upper A Baseline : p 1 minus p 2 less than 0

C. Upper H 0 : p 1 minus p 2 equals 0 Upper H Subscript Upper A Baseline : p 1 minus p 2 not equals 0

D. Upper H 0 : p 1 minus p 2 not equals 0 Upper H Subscript Upper A Baseline : p 1 minus p 2 equals 0

Determine the test statistic. zequals nothing ​(Round to two decimal places as​ needed.) Find the​ P-value. Pequals nothing ​(Round to four decimal places as​ needed.) What is the result of this hypothesis test with a level of significance of 0.1​?

A. Do not reject the null hypothesis because there is not sufficient evidence to support the claim that there is a difference in the proportions of multiple births.

B. Reject the null hypothesis because there is not sufficient evidence to support the claim that there is a difference in the proportions of multiple births.

C. Do not reject the null hypothesis because there is sufficient evidence to support the claim that there is a difference in the proportions of multiple births.

D. Reject the null hypothesis because there is sufficient evidence to support the claim that there is a difference in the proportions of multiple births.

​b) If your conclusion is​ incorrect, which type of error did you​ commit?

A. A Type Upper I error would occur.

B. A Type II error would occur.

C. This cannot be determined without analysis of an actual error.

Answer 1

Let sample 1 is sample of white females

So we have

Sample size=n1=3115

No.of multiple births=x1=146

Sample 2 is sample of black females

Sample size=n2=647

No.of multiple births=x2=22

a)

Since we are interested in testing that if there is difference in the proportion of multiple births in the white and black females or not hence we have

Now calculating test statistics

Sample proportions are given by

Now pooled proportion is given by

Now test is given by

Now since test is two tailed so

Pvalue =2*P(Z>1.45)=2*0.074=0.128

Since P value is higher than level of significance hence we failed to reject H0 hence we Do not have sufficient statistical evidence to conclude that proportions are different.

Hence

Correct option is

A. Do not reject the null hypothesis because there is not sufficient evidence to support the claim that there is a difference in the proportions of multiple births.

b)

Since Type 2 error is defined as falsely accepting H0 since here we are failing to reject H0 hence here we have chance of making type 2 error hence

Correct option is

B. A Type II error would occur.