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hat 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 57 college students were surveyed and 9 of the said that blue is their favorite color lor preference of all college students is different (either way) from that of the general population? Use -0.05. LAUSE SALT (what is the level of significance State the null and alternate hypotheses OM: P-0.24; M₂: P<0.24 OM₂: P-0.24; M₁: P>0.24 OMP 0.34; M₁ -0.24 ⒸMP-0.24; M₁: P0.24 (b) What sampling distribution will you use? O The standard normal, since np5 and n O The standard normal, since np 5 and ng S s O The Student's t, since no 5 and ng S O The Student's t, since np 5 and no s What is the value of the sample test statistic? (Round your answer to two decimal places) (c) Find the 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 04 -1 -2 -1 0 1 D 0-3 0-3 (4) Based on your answers in parts (4) to (c), will you reject or fall to reject the null hypothesis? Are the data statistically significant at level At the 0.05 level, we reject the nul hypothesis and condclude the data are statistically significant Othe-0.05 level, we reject the nul hypothesis and condude the data are not statistically significant At the 0.05 level, we fall to reject the null hypothesis and conclude the data are statistically significant O Althea.05 level, we fall to reject the null hypothesis and conclude the data are not statistically significant 2 1 2 0-3 -2 -1 3 -2 -1 1 0 1 2 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 fevering the color blue differs from 0.24

hat 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 57 college students were surveyed and 9 of the said that blue is their favorite color lor preference of all college students is different (either way) from that of the general population? Use -0.05. LAUSE SALT (what is the level of significance State the null and alternate hypotheses OM: P-0.24; M₂: P<0.24 OM₂: P-0.24; M₁: P>0.24 OMP 0.34; M₁ -0.24 ⒸMP-0.24; M₁: P0.24 (b) What sampling distribution will you use? O The standard normal, since np5 and n O The standard normal, since np 5 and ng S s O The Student's t, since no 5 and ng S O The Student's t, since np 5 and no s What is the value of the sample test statistic? (Round your answer to two decimal places) (c) Find the 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 04 -1 -2 -1 0 1 D 0-3 0-3 (4) Based on your answers in parts (4) to (c), will you reject or fall to reject the null hypothesis? Are the data statistically significant at level At the 0.05 level, we reject the nul hypothesis and condclude the data are statistically significant Othe-0.05 level, we reject the nul hypothesis and condude the data are not statistically significant At the 0.05 level, we fall to reject the null hypothesis and conclude the data are statistically significant O Althea.05 level, we fall to reject the null hypothesis and conclude the data are not statistically significant 2 1 2 0-3 -2 -1 3 -2 -1 1 0 1 2 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 fevering the color blue differs from 0.24

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 13CYU
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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-57 college students were surveyed and r9 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. LA USE SALT (a) What is the level of significance) State the null and alterate hypotheses OM P-0.24; M₁: P<0.24 OHP-0.24; H₁1P>0.24 OMP 0.24; M₁: p= 0.24 ⒸHOP=0.24; H₂P0.24 (b) What sampling distribution will you use? O The standard normal, since np < 5 and ng < 5 5. O The standard normal, since np > 5 and ng > S O The Student's t, since np 5 and ng < 5. O The Student's t, since no 5 and ng S What is the value of the sample test statistic? (Round your answer to two decimal places) (c) Find the 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 -2 -1 0-3 0-3 (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? At the 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the 0.05 level, we fall to reject the null hypothesis and conclude the data are statistically significant. At the a-0.05 level, we fall to reject the null hypothesis and conclude the data are not statistically significant. -2 -1 0 1 0-3 -2 -1 0 1 2 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
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-57 college students were surveyed and r9 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. LA USE SALT (a) What is the level of significance) State the null and alterate hypotheses OM P-0.24; M₁: P<0.24 OHP-0.24; H₁1P>0.24 OMP 0.24; M₁: p= 0.24 ⒸHOP=0.24; H₂P0.24 (b) What sampling distribution will you use? O The standard normal, since np < 5 and ng < 5 5. O The standard normal, since np > 5 and ng > S O The Student's t, since np 5 and ng < 5. O The Student's t, since no 5 and ng S What is the value of the sample test statistic? (Round your answer to two decimal places) (c) Find the 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 -2 -1 0-3 0-3 (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? At the 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the 0.05 level, we fall to reject the null hypothesis and conclude the data are statistically significant. At the a-0.05 level, we fall to reject the null hypothesis and conclude the data are not statistically significant. -2 -1 0 1 0-3 -2 -1 0 1 2 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
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