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. t Suppose a random sample of n = 53 college students were surveyed and r= 11 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. (a) What is the level of significance? State the null and alternate hypotheses. O H: p = 0.24; H,:p < 0.24 O Ho: p = 0.24; H1:p - 0.24 O Ho: p- 0.24; H,: p - 0.24 O Ho:p = 0.24; H,:p > 0.24 (b) What sampling distribution will you use? The Student's t, since np > 5 and ng > 5. The Student's t, since np < 5 and ng < 5. O The standard normal, since np < 5 and ng < 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 -2 1 -1 0 1 2 0 1 2 -2 -2 -1 (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 a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 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.
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. t Suppose a random sample of n = 53 college students were surveyed and r= 11 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. (a) What is the level of significance? State the null and alternate hypotheses. O H: p = 0.24; H,:p < 0.24 O Ho: p = 0.24; H1:p - 0.24 O Ho: p- 0.24; H,: p - 0.24 O Ho:p = 0.24; H,:p > 0.24 (b) What sampling distribution will you use? The Student's t, since np > 5 and ng > 5. The Student's t, since np < 5 and ng < 5. O The standard normal, since np < 5 and ng < 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 -2 1 -1 0 1 2 0 1 2 -2 -2 -1 (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 a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 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.
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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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.t Suppose a random sample of n = 53 college students were surveyed and r= 11 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.
(a) What is the level of significance?
State the null and alternate hypotheses.
O H: p- 0.24; H,:p< 0.24
O Ho: P- 0.24; H: p- 0.24
O Ho: p+ 0.24; H,: p = 0.24
O Ho: p = 0.24; H,:p > 0.24
(b) What sampling distribution will you use?
O The Student's t, since np > 5 and ng > 5.
O The Student's t, since np < 5 and ng < 5.
The standard normal, since np < 5 and ng < 5.
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.
-2
-1
1
2
3
o-3
-2
-1
2
3
-2
o-3
-2
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 a = 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.
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