Would you favor spending more federal tax money on the arts? Of a random sample

Question

Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 212 women, r1 = 67 responded yes. Another random sample of n2 = 177 men showed that r2 = 46 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts? Use = 0.05.

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: p1 = p2; H1: p1 p2H0: p1 = p2; H1: p1 < p2    H0: p1 < p2; H1: p1 = p2H0: p1 = p2; H1: p1 > p2

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume the population distributions are approximately normal.The standard normal. We assume the population distributions are approximately normal.    The Student's t. The number of trials is sufficiently large.The standard normal. The number of trials is sufficiently large.

What is the value of the sample test statistic? (Test the difference p1 p2. Do not use rounded values. Round your final answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?

At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.Fail to reject the null hypothesis, there is insufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.    Reject the null hypothesis, there is sufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.Reject the null hypothesis, there is insufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men

Explanation / Answer

Given that,
sample one, x1 =67, n1 =212, p1= x1/n1=0.316
sample two, x2 =46, n2 =177, p2= x2/n2=0.26
null, Ho: p1 < p2
alternate, H1: p1 > p2
level of significance, = 0.05
from standard normal table,right tailed z /2 =
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.316-0.26)/sqrt((0.29*0.71(1/212+1/177))
zo =1.215
| zo | =1.215
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =1.215 & | z | =1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.2148 ) = 0.11223
hence value of p0.05 < 0.11223,here we do not reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 > p2
test statistic: 1.215
critical value: 1.645
decision: do not reject Ho
p-value: 0.11223

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