Do you prefer paintings in which the people are fully clothed? This question was asked by a professional survey group on behalf of a national arts organization. A random sample of m= 57 people who are conservative voters showed that = 44 said yes. Another random sample of n = 59 people who are liberal voters showed that 2 = 37 said yes. Does this indicate that the population proportion of conservative voters who prefer art with fully clothed people is higher? Use x = 0.05. LUSE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: p₁=p2; H₁: p₁ # p: Ho: p₁=p²; H₁: p₁ < pa (b) What sampling distribution will you use? What assumptions are you making? Ho: pi= p; Hi: pi > p Ho: pip; H₁: p = P2 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. The Student's t. We assume the population distributions are approximately normal. What is the value of the sample test statistic? (Test the difference pi-pz. Do not use rounded values. Round your final answer to two decimal places.)

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LA
P-value
A plot of the sampling distribution curve has a horizontal axis with values from an unidentified negative
value to an unidentified positive value. The curve enters the window from the left, just above the
horizontal axis, goes up and to the right, changes direction over approximately z = 0 on the horizontal axis,
and then goes down and to the right before exiting the window just above the horizontal axis. A point
marked -z is plotted on the horizontal axis to the left of 0. The area under the curve to the left of -z is
shaded.
(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 o ?
At the x = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the x = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically
significant. At the x = 0.05 level, we reject the null hypothesis and conclude the data are
statistically significant. At the x = 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.
Reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters who
prefer art with fully clothed people is higher. Reject the null hypothesis, there is sufficient evidence
that the proportion of conservative voters who prefer art with fully clothed people is higher.
reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters who
prefer art with fully clothed people is higher. Fail to reject the null hypothesis, there is insufficient
evidence that the proportion of conservative voters who prefer art with fully clothed people is higher.
Fail to
Transcribed Image Text:LA P-value A plot of the sampling distribution curve has a horizontal axis with values from an unidentified negative value to an unidentified positive value. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately z = 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. A point marked -z is plotted on the horizontal axis to the left of 0. The area under the curve to the left of -z is shaded. (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 o ? At the x = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the x = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the x = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the x = 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. Reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters who prefer art with fully clothed people is higher. Reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters who prefer art with fully clothed people is higher. reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters who prefer art with fully clothed people is higher. Fail to reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters who prefer art with fully clothed people is higher. Fail to
6
Do you prefer paintings in which the people are fully clothed? This question was asked by a professional
survey group on behalf of a national arts organization. A random sample of m= 57 people who are
conservative voters showed that ₁ = 44 said yes. Another random sample of m2 = 59 people who are
liberal voters showed that 2 = 37 said yes. Does this indicate that the population proportion of
conservative voters who prefer art with fully clothed people is higher? Use x = 0.05.
USE SALT
(a)
What is the level of significance?
State the null and alternate hypotheses.
O
O
Ho: pi= p; H₁: p₁ p. Ho: pi= p; H₁: p₁ < p₂
(b)
What sampling distribution will you use? What assumptions are you making?
Ho: p = pz; H₁: p₁>p₂ Ho: pi > pz; H₁: p₁ = P₂
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. The Student's t. We assume the population distributions are approximately normal.
What is the value of the sample test statistic? (Test the difference p-p₂. Do not use rounded values.
Round your answer 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.
A
0
P-value
A plot of the sampling distribution curve has a horizontal axis with values from an unidentified negative
value to an unidentified positive value. The curve enters the window from the left, just above the
horizontal axis, goes up and to the right, changes direction over approximately z = 0 on the horizontal axis,
and then goes down and to the right before exiting the window just above the horizontal axis. A point
marked z is plotted on the horizontal axis to the right of 0. The area under the curve to the right of z is
Transcribed Image Text:6 Do you prefer paintings in which the people are fully clothed? This question was asked by a professional survey group on behalf of a national arts organization. A random sample of m= 57 people who are conservative voters showed that ₁ = 44 said yes. Another random sample of m2 = 59 people who are liberal voters showed that 2 = 37 said yes. Does this indicate that the population proportion of conservative voters who prefer art with fully clothed people is higher? Use x = 0.05. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O O Ho: pi= p; H₁: p₁ p. Ho: pi= p; H₁: p₁ < p₂ (b) What sampling distribution will you use? What assumptions are you making? Ho: p = pz; H₁: p₁>p₂ Ho: pi > pz; H₁: p₁ = P₂ 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. The Student's t. We assume the population distributions are approximately normal. What is the value of the sample test statistic? (Test the difference p-p₂. Do not use rounded values. Round your answer 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. A 0 P-value A plot of the sampling distribution curve has a horizontal axis with values from an unidentified negative value to an unidentified positive value. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately z = 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. A point marked z is plotted on the horizontal axis to the right of 0. The area under the curve to the right of z is
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