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In Country A the population mean height for 3-year-old boys is 37 inches. Suppose a random sample of 15 3-year-old boys from Country B showed a sample mean of 36.8 inches with a standard deviation of 2 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. Complete parts a through c a. Determine whether the population mean for Country B boys is significantly different from the Country A mean. Use a significance level of 0.05. Which of the following correctly states Ho and H,? Họ 37 H37 OB Hs37 Ho 2 37 OC. He37 OA. Họ: 37 OD. Hip37 O :37 Hi 37 H37 Find the test statistic t -0.39 (Type an integer or decimal rounded to two decimal places as needed.) Find the pvalue. p- 0.702 (Type an integer or decimal rounded to three decimal places as needed.) Reject or do not reject H. Choose the correct answer below. A. Do not reject Hg. There is no reason to believe that 37 in. is not the population mean at a significance level of 0.05 OB. Do not reject H. The population mean is definitely 37 in. on the basis of these data at a significance level of 0.05. OC. Reject Ho. There is reason to believe that 37 in. is not population mean at a significance level of 0.05. OD. Reject H. The population mean is definitely not 37 in, on the basis of these data at a significance level of 0.05. b. Now suppose the sample consists of 30 boys instead of 15 and repeat the test. Find the test statistic t- -0.55 (Type an integer or decimal rounded to two decimal places as needed.) Find the p-value. (Type an integer or decimal rounded to three decimal places as needed.)

In Country A the population mean height for 3-year-old boys is 37 inches. Suppose a random sample of 15 3-year-old boys from Country B showed a sample mean of 36.8 inches with a standard deviation of 2 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population. Complete parts a through c a. Determine whether the population mean for Country B boys is significantly different from the Country A mean. Use a significance level of 0.05. Which of the following correctly states Ho and H,? Họ 37 H37 OB Hs37 Ho 2 37 OC. He37 OA. Họ: 37 OD. Hip37 O :37 Hi 37 H37 Find the test statistic t -0.39 (Type an integer or decimal rounded to two decimal places as needed.) Find the pvalue. p- 0.702 (Type an integer or decimal rounded to three decimal places as needed.) Reject or do not reject H. Choose the correct answer below. A. Do not reject Hg. There is no reason to believe that 37 in. is not the population mean at a significance level of 0.05 OB. Do not reject H. The population mean is definitely 37 in. on the basis of these data at a significance level of 0.05. OC. Reject Ho. There is reason to believe that 37 in. is not population mean at a significance level of 0.05. OD. Reject H. The population mean is definitely not 37 in, on the basis of these data at a significance level of 0.05. b. Now suppose the sample consists of 30 boys instead of 15 and repeat the test. Find the test statistic t- -0.55 (Type an integer or decimal rounded to two decimal places as needed.) Find the p-value. (Type an integer or decimal rounded to three decimal places as needed.)

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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In an educational exercise, we are tasked with determining whether the population mean height for 3-year-old boys in Country B is significantly different from the population mean height in Country A, which is 37 inches. Given data includes a random sample of 15 boys from Country B, exhibiting a sample mean of 36.8 inches and a standard deviation of 2 inches. The significance level is set at 0.05, and the assumptions include independent sampling and normally distributed heights in the population. ### Hypothesis Testing **Hypotheses Setup:** - Null Hypothesis (H₀): μ = 37 - Alternative Hypothesis (H₁): μ ≠ 37 **Selected Correct Hypothesis:** - H₀: μ = 37 - H₁: μ ≠ 37 **Test Statistic Calculation:** - Calculated test statistic \( t = -0.39 \) **P-Value:** - Calculated p-value \( p = 0.702 \) **Decision Rule:** - Consider whether to reject H₀ based on the p-value. Given the p-value is greater than the significance level of 0.05, the decision is: - Do not reject H₀. There is no reason to believe that 37 inches is not the population mean at a significance level of 0.05. ### Analysis with Increased Sample Size **Suppose a new sample consists of 30 boys, and the test is repeated.** **Test Statistic Calculation:** - New calculated test statistic \( t = -0.55 \) **P-Value:** - New calculated p-value \( p = \) (The p-value needs to be provided.) This exercise demonstrates the application of hypothesis testing in evaluating population means, using sample data to make inferences about a larger population.
Transcribed Image Text:In an educational exercise, we are tasked with determining whether the population mean height for 3-year-old boys in Country B is significantly different from the population mean height in Country A, which is 37 inches. Given data includes a random sample of 15 boys from Country B, exhibiting a sample mean of 36.8 inches and a standard deviation of 2 inches. The significance level is set at 0.05, and the assumptions include independent sampling and normally distributed heights in the population. ### Hypothesis Testing **Hypotheses Setup:** - Null Hypothesis (H₀): μ = 37 - Alternative Hypothesis (H₁): μ ≠ 37 **Selected Correct Hypothesis:** - H₀: μ = 37 - H₁: μ ≠ 37 **Test Statistic Calculation:** - Calculated test statistic \( t = -0.39 \) **P-Value:** - Calculated p-value \( p = 0.702 \) **Decision Rule:** - Consider whether to reject H₀ based on the p-value. Given the p-value is greater than the significance level of 0.05, the decision is: - Do not reject H₀. There is no reason to believe that 37 inches is not the population mean at a significance level of 0.05. ### Analysis with Increased Sample Size **Suppose a new sample consists of 30 boys, and the test is repeated.** **Test Statistic Calculation:** - New calculated test statistic \( t = -0.55 \) **P-Value:** - New calculated p-value \( p = \) (The p-value needs to be provided.) This exercise demonstrates the application of hypothesis testing in evaluating population means, using sample data to make inferences about a larger population.
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