Question

In

1993

a reproductive clinic reported

41

live births to

166

women under the age of​ 38, but only

6

live births for

74

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.

​a) 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.

Upper H 0 : p 1 minus p 2 not equals 0H0: p1−p2≠0

Upper H Subscript Upper A Baseline : p 1 minus p 2 equals 0HA: p1−p2=0

B.

Upper H 0 : p 1 minus p 2 not equals 0H0: p1−p2≠0

Upper H Subscript Upper A Baseline : p 1 minus p 2 greater than 0HA: p1−p2>0

C.

Upper H 0 : p 1 minus p 2 equals 0H0: p1−p2=0

Upper H Subscript Upper A Baseline : p 1 minus p 2 less than 0HA: p1−p2<0

D.

Upper H 0 : p 1 minus p 2 equals 0H0: p1−p2=0

Upper H Subscript Upper A Baseline : p 1 minus p 2 not equals 0HA: p1−p2≠0

Your answer is correct.

Determine the test statistic.

zequals=3.12

​(Round to two decimal places as​ needed.)

Find the​ P-value.

Pequals=0.0018

​(Round to four decimal places as​ needed.)

What is the result of this hypothesis test at a level of significance of

0.01?

A.

Do not rejectDo not reject

the null hypothesis because there

isis

sufficient evidence to support the claim that there is a difference in the effectiveness of the methods.

B.

Do not rejectDo not reject

the null hypothesis because there

is notis not

sufficient evidence to support the claim that there is a difference in the effectiveness of the methods.

C.

RejectReject

the null hypothesis because there

isis

sufficient evidence to support the claim that there is a difference in the effectiveness of the methods.Your answer is correct.

D.

RejectReject

the null hypothesis because there

is notis not

sufficient evidence to support the claim that there is a difference in the effectiveness of the methods.

​b) If you concluded there was a​ difference, estimate that​ difference,

p1minus−p2​,

with a

99​%

confidence interval. Select the correct answer below​ and, if​ necessary, fill in the answer boxes within your choice.

A.The confidence interval is

left parenthesis nothing comma nothing right parenthes

​(Round to three decimal places as​ needed.)

B.

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.

Answer 1

Given that, n1 = 166 and x1 = 41

n2 = 74 ans x2 = 6

The null and the alternative hypotheses are,

H0: p1−p2=0

HA: p1−p2≠0

Using TI-84 calculator we get,

Test statistic is, z = 2.99

p-value =0.0028

Here, p-value = 0.0028 < 0.01 level of significance,

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

b) 95% confidence interval for ( p1 - p2) is,

( 0.076, 0.256)

since, zero is not lie in above interval we conclude that, there is a difference in the effectiveness of the methods.