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What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24 of the population claim blue as their favorite color.+ Suppose a random sample of n = 59 college students were surveyed and r = 10 of them said that blue is their favorite color. Does this information mply that the color preference of all college students i different (either way) from that of the general population? Use a = 0.05. LUSE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: P = 0.24; H₁: p > 0.24 O Ho: P = 0.24; H₁: p < 0.24 O Ho: P = 0.24; H₁: P = 0.24 O Ho: P = 0.24; H₁: p = 0.24 (b) What sampling distribution will you use? O The Student's t, since np < 5 and nq < 5. O The standard normal, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq > 5. O The standard normal, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.

What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24 of the population claim blue as their favorite color.+ Suppose a random sample of n = 59 college students were surveyed and r = 10 of them said that blue is their favorite color. Does this information mply that the color preference of all college students i different (either way) from that of the general population? Use a = 0.05. LUSE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: P = 0.24; H₁: p > 0.24 O Ho: P = 0.24; H₁: p < 0.24 O Ho: P = 0.24; H₁: P = 0.24 O Ho: P = 0.24; H₁: p = 0.24 (b) What sampling distribution will you use? O The Student's t, since np < 5 and nq < 5. O The standard normal, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq > 5. O The standard normal, since np > 5 and nq > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.+ Suppose a random sample of n = 59 college students were surveyed and r = 10 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use a = 0.05. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: P = 0.24; H₁: p > 0.24 O Ho: P = 0.24; H₁: p < 0.24 O Ho: P = 0.24; H₁: P = 0.24 O Ho: P = 0.24; H₁: p = 0.24 (b) What sampling distribution will you use? O The Student's t, since np < 5 and nq < 5. O The standard normal, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq > 5. O The standard normal, since np > 5 and ng > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.
Transcribed Image Text:What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.+ Suppose a random sample of n = 59 college students were surveyed and r = 10 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use a = 0.05. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: P = 0.24; H₁: p > 0.24 O Ho: P = 0.24; H₁: p < 0.24 O Ho: P = 0.24; H₁: P = 0.24 O Ho: P = 0.24; H₁: p = 0.24 (b) What sampling distribution will you use? O The Student's t, since np < 5 and nq < 5. O The standard normal, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq > 5. O The standard normal, since np > 5 and ng > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.
0-3 -3 -2 -1 -2 Read It -1 0 1 0 Watch It 2 1 ^^ 3 0-3 -2 3 2 0-3 -1 0 -1 1 0 2 1 2 3 (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 a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 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 statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 3 (e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24. O There is insufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24. Need Help?
Transcribed Image Text:0-3 -3 -2 -1 -2 Read It -1 0 1 0 Watch It 2 1 ^^ 3 0-3 -2 3 2 0-3 -1 0 -1 1 0 2 1 2 3 (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 a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 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 statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. 3 (e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24. O There is insufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24. Need Help?
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