Would you favor spending more federal tax money on the arts? Of a random sample of n₁208 women, r53 responded yes. Another random sample of n₂ 169 men showed that r₂ = 50 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion men who favor spending more federal tax dollars on the arts? Use a = 0.05. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O : Pg < Pa! HaPp = Pa Ho! P1 P₂² H₁: P1 P₂ O Hoi Pq Pyl Hy! Pg » P₂ O Mg} P: * Pg} Hg: P: *P? (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume the population distributions are approximately normal. O The Student's t. We assume the population distributions are approximately normal. O The standard normal. The number of trials is sufficiently large. O The Student's t. 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.)

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Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 208 women, r₁= 53 responded yes. Another random sample of n₂ = 169 men showed that r₂ = 50 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 α = 0.05.
USE SALT
(a) What is the level of significance?
State the null and alternate hypotheses.
Ho: P₁ P₂ H₁² P₁ = P₂
O Ho: P₁ = P₂² H₁: P₁ < P2
O Ho: P₁ = P₂² H₁² P₁ > P₂
O Ho: P₁ = P₂² H₂i Pq # P2
(b) What sampling distribution will you use? What assumptions are you making?
O The standard normal. We assume the population distributions are approximately normal.
O The Student's t. We assume the population distributions are approximately normal.
O The standard normal. The number of trials is sufficiently large.
O The Student's t. 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.)
Transcribed Image Text:Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 208 women, r₁= 53 responded yes. Another random sample of n₂ = 169 men showed that r₂ = 50 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 α = 0.05. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: P₁ P₂ H₁² P₁ = P₂ O Ho: P₁ = P₂² H₁: P₁ < P2 O Ho: P₁ = P₂² H₁² P₁ > P₂ O Ho: P₁ = P₂² H₂i Pq # P2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume the population distributions are approximately normal. O The Student's t. We assume the population distributions are approximately normal. O The standard normal. The number of trials is sufficiently large. O The Student's t. 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.
M
O
Z
P-value
P-value
O
P-value
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 a?
O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(e) Interpret your conclusion in the context of the application.
O 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.
O 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.
O 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.
O 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.
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value. M O Z P-value P-value O P-value 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 a? O At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. O 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. O 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. O 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. O 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.
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