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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

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Title: Hypothesis Testing for Favorite Color Preference** **Background:** A large survey of countries including the United States, China, Russia, France, Turkey, Kenya, and others indicates that most people prefer the color blue. About 24% of the population claim blue as their favorite color. **Scenario:** A random sample of \( n = 57 \) college students was surveyed, and \( x = 17 \) of them said blue is their favorite color. Does this imply that the preference of college students is different from that of the general population? --- **Question 1(a):** What is the level of significance? **Options:** - \( \alpha = 0.01 \) - \( \alpha = 0.05 \) - \( \alpha = 0.10 \) **Hypotheses:** - Null Hypothesis \( H_0: p = 0.24 \) - Alternative Hypothesis \( H_a: p \neq 0.24 \) **Question 1(b):** What sampling distribution will you use? Options: 1. The standard normal, since \( np > 5 \) and \( nq > 5 \). 2. The standard normal, since \( n > 30 \). 3. The Student's \( t \), since \( n \leq 30 \) and \( \sigma \) is unknown. 4. The Student's \( t \), since \( np \leq 5 \). **What is the value of the sample test statistic?** **Question 1(c):** Find the P-value of the test statistic. Round your answer to four decimal places. **Diagrams:** There are four graphs displaying normal distributions with shaded areas under the curve, representative of P-values. 1. Graph A (shows left tail) 2. Graph B (shows right tail) 3. Graph C (symmetrical, both tails) 4. Graph D (centered, no clear tails) **Question 1(d):** Based on your answers, should you reject or fail to reject the null hypothesis? Options: - Fail to reject \( H_0 \) - Reject \( H_0 \) --- **Conclusion:** This exercise investigates whether the preference for the color blue in college students is statistically different from the general population's preference. Follow the steps of hypothesis testing to determine the outcome.
Transcribed Image Text:**Title: Hypothesis Testing for Favorite Color Preference** **Background:** A large survey of countries including the United States, China, Russia, France, Turkey, Kenya, and others indicates that most people prefer the color blue. About 24% of the population claim blue as their favorite color. **Scenario:** A random sample of \( n = 57 \) college students was surveyed, and \( x = 17 \) of them said blue is their favorite color. Does this imply that the preference of college students is different from that of the general population? --- **Question 1(a):** What is the level of significance? **Options:** - \( \alpha = 0.01 \) - \( \alpha = 0.05 \) - \( \alpha = 0.10 \) **Hypotheses:** - Null Hypothesis \( H_0: p = 0.24 \) - Alternative Hypothesis \( H_a: p \neq 0.24 \) **Question 1(b):** What sampling distribution will you use? Options: 1. The standard normal, since \( np > 5 \) and \( nq > 5 \). 2. The standard normal, since \( n > 30 \). 3. The Student's \( t \), since \( n \leq 30 \) and \( \sigma \) is unknown. 4. The Student's \( t \), since \( np \leq 5 \). **What is the value of the sample test statistic?** **Question 1(c):** Find the P-value of the test statistic. Round your answer to four decimal places. **Diagrams:** There are four graphs displaying normal distributions with shaded areas under the curve, representative of P-values. 1. Graph A (shows left tail) 2. Graph B (shows right tail) 3. Graph C (symmetrical, both tails) 4. Graph D (centered, no clear tails) **Question 1(d):** Based on your answers, should you reject or fail to reject the null hypothesis? Options: - Fail to reject \( H_0 \) - Reject \( H_0 \) --- **Conclusion:** This exercise investigates whether the preference for the color blue in college students is statistically different from the general population's preference. Follow the steps of hypothesis testing to determine the outcome.
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