A study investigated whether regular mammograms resulted in fewer deaths from breast cancer over a period of

1818

years. Among

30 comma 63330,633

women who never had mammograms,

183183

died of breast cancer, while only

147147

of

30 comma 11730,117

who had undergone screening died of breast cancer.

a) Do these results suggest that mammograms may be an effective screening tool to reduce breast cancer deaths?

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

Question content area bottom

Part 1

a) Let

pSubscript1

be the proportion of deaths for women who had never had a mammogram and

pSubscript2

be the proportion of deaths for women who had undergone screening. 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

Upper H 0 : p 1 minus p 2 equals 0H0:p1p2=0

Upper H Subscript Upper A Baseline : p 1 minus p 2 greater than 0HA:p1p2>0

Your answer is correct.

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

Upper H 0 : p 1 minus p 2 not equals 0H0:p1p20

Upper H Subscript Upper A Baseline : p 1 minus p 2 equals 0HA:p1p2=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

Upper H 0 : p 1 minus p 2 equals 0H0:p1p2=0

Upper H Subscript Upper A Baseline : p 1 minus p 2 not equals 0HA:p1p20

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

Upper H 0 : p 1 minus p 2 greater than 0H0:p1p2>0

Upper H Subscript Upper A Baseline : p 1 minus p 2 less than 0HA:p1p2<0

Part 2

Determine the test statistic.

zequals=1.831.83

(Round to two decimal places as needed.)

Part 3

Find the P-value.

Pequals=0.03330.0333

(Round to four decimal places as needed.)

Part 4

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

0.10.1?

A.

Do not rejectDonotreject

the null hypothesis because there

is notisnot

sufficient evidence to support the claim that screening reduces the proportion of deaths.

B.

Do not rejectDonotreject

the null hypothesis because there

isis

sufficient evidence to support the claim that screening reduces the proportion of deaths.

C.

RejectReject

the null hypothesis because there

isis

sufficient evidence to support the claim that screening reduces the proportion of deaths.

Your answer is correct.

D.

RejectReject

the null hypothesis because there

is notisnot

sufficient evidence to support the claim that screening reduces the proportion of deaths.

Part 5

b) Determine the type of error committed if your conclusion is incorrect.

A.

A Type

IIII

error could occur.

B.

This cannot be determined without analysis of an actual error.

Your answer is not correct.

C.

A Type

Upper II

error could occur.