Question

In a​ survey, respondents were​ asked, "Would you be willing to pay higher taxes if the tax revenue went directly toward deficit​ reduction?" Treat the respondents as a simple random sample of adults. Complete parts​ (a) and​ (b).

DATA

Gender   Response
Male   Yes
Female   No
Female   Yes
Female   No
Male   No
Female   No
Male   No
Male   No
Female   No
Male   Yes
Male   Yes
Female   No
Female   No
Male   Yes
Male   No
Female   Yes
Male   No
Male   No
Female   Yes
Female   No
Female   No
Male   Yes
Female   No
Male   Yes
Male   No
Female   No
Female   No
Male   Yes
Female   No
Male   No
Male   No
Male   No
Female   No
Female   No
Male   No
Female   No
Female   No
Male   No
Male   No
Male   No
Female   No
Male   No
Female   No
Male   No
Female   No
Male   No
Male   No
Male   No
Male   No
Male   No
Male   Yes
Female   No
Female   Yes
Female   No
Male   No
Female   No
Male   No
Male   No
Female   No
Male   Yes
Male   Yes
Female   No
Female   No
Male   Yes
Male   No
Female   Yes
Male   No
Male   No
Female   Yes
Female   No
Female   No
Male   Yes
Female   No
Male   Yes
Male   No
Female   No
Female   No
Male   Yes
Female   No
Male   No
Male   No
Male   No
Female   No
Female   No
Male   No
Female   No
Female   No
Male   No
Male   No
Male   No
Female   No
Male   No
Female   No
Male   No
Female   No
Male   No
Male   No
Male   No
Male   No
Male   No
Male   Yes
Female   No
Female   Yes
Female   No
Male   No
Female   No
Male   No
Male   No
Female   No
Male   Yes
Male   Yes
Female   No
Female   No
Male   Yes
Male   No
Female   Yes
Male   No
Male   No
Female   Yes
Female   No
Female   No
Male   Yes
Female   No
Male   Yes
Male   No
Female   No
Female   No
Male   Yes
Female   No
Male   No
Male   No
Male   No
Female   No
Female   No
Male   No
Female   No
Female   No
Male   No
Male   No
Male   No
Female   No
Male   No
Female   No
Male   No
Female   No
Male   No
Male   No
Male   No
Male   No
Male   No
Male   Yes
Female   No
Female   Yes
Female   No
Male   No
Female   No
Male   No
Male   No
Female   No
Male   Yes
Male   Yes
Female   No
Female   No
Male   Yes
Male   No
Female   Yes
Male   No
Male   No
Female   Yes
Female   No
Female   No
Male   Yes
Female   No
Male   Yes
Male   No
Female   No
Female   No
Male   Yes
Female   No
Male   No
Male   No
Male   No
Female   No
Female   No
Male   No
Female   No
Female   No
Male   No
Male   No
Male   No
Female   No
Male   No
Female   No
Male   No
Female   No
Male   No
Male   No
Male   No
Male   No
Male   No

a. What proportion of the males who took the survey is willing to pay higher taxes to reduce the​ deficit? What proportion of the females who took the survey is willing to pay higher taxes to reduce the​ deficit?

The proportions of the males and females who took the survey who are willing to pay higher taxes to reduce the deficit are BLANK and BLANK​,respectively.

b. Is there significant evidence to suggest the proportions of males and females who are willing to pay higher taxes to reduce the deficit differ at the a=0.05 level of​ significance?

First verify the model requirements. Select all that apply.

A. The data come from a population that is normally distributed.

B.The sample size is more than​ 5% of the population size for each sample.

C.The sample size is less than​ 5% of the population size for each sample.

D.The samples are dependent.

E.The samples are independent.

c. Is there a difference in how males and females feel about paying more taxes to reduce the​ deficit? Identify the null and alternative hypotheses for this test. Let p1 represent the population proportion of adult males who are willing to pay higher taxes to reduce the deficit and p2 represent the population proportion of adult females who are willing to pay higher taxes to reduce the deficit.

Determine the null and alternative hypotheses.

H0:p1 (=,≠,>,<) p2

H1:p1 (=,≠,>,<) p2

d. Find the test statistic for this hypothesis test.

e. Determine the​ P-value for this hypothesis test.

f. Interpret the​ P-value.

If the population proportions are (equal, not equal) one would expect a sample difference proportion (greater than, as extreme or more extrem than, less than, equal to) the one observed in about BLANK out of 100 repetitions of this experiment.

g. State the conclusion for this hypothesis test.

A. Do not reject H0. There is sufficient evidence at the a=0.05 level of significance to suggest the proportions of males and females who are willing to pay higher taxes to reduce the deficit differ.

B. Do not reject H0. There is not sufficient evidence at the a=0.05 level of significance to suggest the proportions of males and females who are willing to pay higher taxes to reduce the deficit differ.

C. Reject Upper H0. There is sufficient evidence at the a=0.05 level of significance to suggest the proportions of males and females who are willing to pay higher taxes to reduce the deficit differ.

D. Reject Upper H0.Thereis not sufficient evidence at the a=0.05 level of significance to suggest the proportions of males and females who are willing to pay higher taxes to reduce the deficit differ.

Answer 1

(a) Proportion of the males = 0.25

Proportion of the females = 0.136364

(b) A. The data come from a population that is normally distributed.

C.The sample size is less than​ 5% of the population size for each sample.

E.The samples are independent.

(c) H0: p1 = p2

Ha: p1 ≠ p2

(d)

1.99

z

(e)

.0461

p-value (two-tailed)

(f) If the population proportions are (not equal) one would expect a sample difference proportion (as extreme or more extrem than) the one observed in about 5 out of 100 repetitions of this experiment.

(g) C. Reject Upper H0. There is sufficient evidence at the a=0.05 level of significance to suggest the proportions of males and females who are willing to pay higher taxes to reduce the deficit differ.

	Male	Female	Total
Yes	28	12	40
No	84	76	160
Total	112	88	200

p1	p2	pc
0.25	0.1364	0.2	p (as decimal)
28/112	12/88	40/200	p (as fraction)
28.	12.	40.	X
112	88	200	n
	0.1136	difference
	0.	hypothesized difference
	0.057	std. error
	1.99	z
	.0461	p-value (two-tailed)

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