Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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C. Find p value D. Make a decision
**Automobiles Purchased** An automobile owner found that 20 years ago, 74% of Americans said that they would prefer to purchase an American automobile. He believes that the number is much greater than 74% today. He selected a random sample of 48 Americans and found that 42 said that they would prefer an American automobile. Can it be concluded that the percentage today is greater than 74%? At a significance level of α = 0.05, is he correct? Use the critical value method with tables. Do not round intermediate steps. ### Part 1 of 5 (a) **State the hypotheses and identify the claim.** Null Hypothesis \( H_0: p = 0.74 \) not claim Alternative Hypothesis \( H_1: p > 0.74 \) claim This hypothesis test is a one-tailed test. **Alternate Answer:** \( H_0: p = 0.74 \) not claim \( H_1: p > 0.74 \) claim This hypothesis test is a one-tailed test. **Graph Explanation** This section involves setting up hypotheses for a single population proportion test, with a primary focus on understanding whether the current preference exceeds the historical figure of 74%. The graph associated with these hypotheses would likely depict the critical region relevant to the one-tailed test at the 0.05 significance level. ### Part 2 of 5 (b) **Find the critical value(s).** Round the answer to two decimal places. If there is more than one critical value, separate them with commas. **Critical value(s):** [Input Box] The critical value(s) will determine the threshold at which we reject the null hypothesis, based on standard statistical tables for a Z-distribution at the given significance level.
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Transcribed Image Text:**Automobiles Purchased** An automobile owner found that 20 years ago, 74% of Americans said that they would prefer to purchase an American automobile. He believes that the number is much greater than 74% today. He selected a random sample of 48 Americans and found that 42 said that they would prefer an American automobile. Can it be concluded that the percentage today is greater than 74%? At a significance level of α = 0.05, is he correct? Use the critical value method with tables. Do not round intermediate steps. ### Part 1 of 5 (a) **State the hypotheses and identify the claim.** Null Hypothesis \( H_0: p = 0.74 \) not claim Alternative Hypothesis \( H_1: p > 0.74 \) claim This hypothesis test is a one-tailed test. **Alternate Answer:** \( H_0: p = 0.74 \) not claim \( H_1: p > 0.74 \) claim This hypothesis test is a one-tailed test. **Graph Explanation** This section involves setting up hypotheses for a single population proportion test, with a primary focus on understanding whether the current preference exceeds the historical figure of 74%. The graph associated with these hypotheses would likely depict the critical region relevant to the one-tailed test at the 0.05 significance level. ### Part 2 of 5 (b) **Find the critical value(s).** Round the answer to two decimal places. If there is more than one critical value, separate them with commas. **Critical value(s):** [Input Box] The critical value(s) will determine the threshold at which we reject the null hypothesis, based on standard statistical tables for a Z-distribution at the given significance level.
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