Question

Radioactive fallout from testing atomic bombs drifted across a region. There were 220 people in the region at the time and 39 of them eventually died of cancer. Cancer experts estimate that one would expect only about 33 cancer deaths in a group this size. Assume the sample is a typical group of people.

a​) Are the assumptions and the conditions to perform a​ one-proportion z-test​ met? yes or no

State the null and alternative hypotheses. Choose the correct answer below.

A.H0​:p=0.1500

HA​:p<0.1500

B.H0​:p=0.1500

HA​:p≠0.1500

C.H0​:p=0.1500

HA​:p>0.1500

D.The assumptions and conditions are not​ met, so the test cannot proceed.

Determine the​ z-test statistic. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.zequals=___

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

B.The assumptions and conditions are not​ met, so the test cannot proceed.

Find the​ P-value. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.P-value=___

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

B.The assumptions and conditions are not​ met, so the test cannot proceed.

Is the observed death rate unusually​ high? Choose the correct answer below.

A.The​ P-value is low enoughlow enough to conclude that the death rate is unusually high.

B.The​ P-value is too hightoo high to conclude that the death rate is unusually high.

C.The​ P-value is high enough to conclude that the death rate is unusually high.

D.The assumptions and conditions are not​ met, so the test cannot proceed.

​b) Does this prove that exposure to radiation increases the risk of​ cancer? Choose the correct answer below.

A.Whether the death rate by cancer is unusually high or​ not, the cause cannot be determined.

B.​No, there is insufficient evidence to conclude that exposure to radiation increases the risk of cancer.

C.Yes, there is sufficient evidence to conclude that exposure to radiation increases the risk of cancer.

D.The assumptions and conditions are not​ met, so the test cannot proceed.

Answer 1

a)yes

=

C.H0​:p=0.1500

HA​:p>0.150

std error   se =√(p*(1-p)/n) =		0.0252
sample proportion p̂ = x/n=		0.1950

test stat z =(p̂-p)/√(p(1-p)/n)=

1.78

p value                          =

0.0375

A.The​ P-value is low enough to conclude that the death rate is unusually high.

b)

A.Whether the death rate by cancer is unusually high or​ not, the cause cannot be determined.