Question

In a survey of 9600 twelfth grade​ males, 2314 said they had smoked in the last 30 days. In a survey of 5300 twelfth grade​ females, 964 said they had smoked in the last 30 days. At α=0.05 can you support the claim that the proportion of twelfth grade males who said they had smoked in the last 30 days is less than the proportion of twelfth grade females who said they had smoked in the last 30​ days? Assume the random samples are independent. Complete parts​ (a) through​ (e).

​(a) Identify the claim and state

Upper H0 and Upper Ha.

The claim is​ "the proportion of twelfth grade males who said they had smoked in the last 30 days is less than/the same as/different than/greater than the proportion of twelfth grade​ females."

Let p1 and p2 be the two population proportions. State H0 and Ha.

Choose the correct answer below.

A. H0​: p1≠p2

Ha​: p1=p2

B. H0​: p1 < p2

Ha​: p1 ≥ p2

C. H0​: p1 ≤ p2

Ha​: p1 > p2

D. H0​: p1 > p2

Ha​: p1 ≤ p2

E. H0​: p1 = p2

Ha​: p1 ≠ p2

F. H0​: p1 ≥ p2

Ha​: p1 < p2

(b) Find the critical​ value(s) and identify the rejection​ region(s).

z0= ___________

​(Use a comma to separate answers as needed. Type an integer or a decimal. Round to three decimal places as​ needed.)

Identify the rejection​ region(s). Choose the correct answer below.

A. z < −1.96

B.z greater than or equal to −1.645

C. z < −1.96

z >1.96

D. z < −1.645

E. z < −1.645

z >1.645

F. z > -1.96

(c) Find the standardized test statistic.

z= ____________ ​(Round to two decimal places as​ needed.)

d) Decide whether to reject or fail to reject the null hypothesis.

Choose the correct answer below.

a. Fail to reject H0

b. Reject H0.

​(e) Interpret the decision in the context of the original claim.

Choose the correct answer below.

A.At the 5​% significance​ level, there is insufficient evidence to support the claim.

B.At the 5​% significance​ level, there is sufficient evidence to reject the claim.

C.At the 5​% significance​ level, there is sufficient evidence to support the claim.

D.At the 5​% significance​ level, there is insufficient evidence to reject the claim.

Answer 1

(a) The correct answer for null and alternative hypothesis is (F), i.e.,

Let, : proportion of twelfth grade males who said they had smoked in the last 30 days.

: proportion of twelfth grade females who said they had smoked in the last 30 days.

Claim: "the proportion of twelfth grade males who said they had smoked in the last 30 days is less than the proportion of twelfth grade​ females who said they had smoked in the last 30 days."

_______________________________________

(b) Since it is a Left-tailed hypothesis and the significance level is given as

Critical value:

The correct option for rejection region is (D), i.e.,

So, we reject the null hypothesis, if the test-statistic is less than the critical value of -1.64, i.e.,

____________________________________________

(c) The formula for the test-statistic is:

(Sample proportion of males who said they had smoked in the last 30 days.)

(Sample proportion of females who said they had smoked in the last 30 days.)

So, the standardized test-statistic is calculated as

_____________________________________________

(d) The correct option is (a), i.e., Fail to reject H₀

and the test-statistic is

Since,

___________________________________

(e) The correct interpretation is (A), i.e., At the 5​% significance​ level, there is insufficient evidence to support the claim.