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In Country A, the population mean height for 10-year-old girls is 54.9 inches with a standard deviation of 1.9 inches. Suppose a random sample of 15 10-year-old girls from Country B is taken and that these girls had a sample mean height of 53.6 inches with a standard deviation of 2.2 inches. Assume that heights are Normally distributed. Complete parts (a) through (c) below. a. Determine whether the population mean for height for 10-year-old girls from Country B is significantly different from the Country A population mean. Use a significance level of 0.05. Determine the null and alternative hypotheses. Choose the correct answer below. A. Ho: μ = 54.9 Ha:μ> 54.9 D. Ho: μ> 54.9 H₂:μ = 54.9 The sample Check the conditions to see whether the test statistic will follow a t-distribution. p= B. Ho: μ = 54.9 Ha: μ#54.9 Find the test statistic. E. Ho: μ = 54.9 Ha: μ< 54.9 t= -2.29 (Round to two decimal places as needed.) Find the p-value. is random and the observations are independent. The distribution of the heights is Normally distributed. C. Ho: μ#54.9 Ha: μ = 54.9 (Round to three decimal places as needed.) F. Ho: μ<54.9 Ha: μ = 54.9

In Country A, the population mean height for 10-year-old girls is 54.9 inches with a standard deviation of 1.9 inches. Suppose a random sample of 15 10-year-old girls from Country B is taken and that these girls had a sample mean height of 53.6 inches with a standard deviation of 2.2 inches. Assume that heights are Normally distributed. Complete parts (a) through (c) below. a. Determine whether the population mean for height for 10-year-old girls from Country B is significantly different from the Country A population mean. Use a significance level of 0.05. Determine the null and alternative hypotheses. Choose the correct answer below. A. Ho: μ = 54.9 Ha:μ> 54.9 D. Ho: μ> 54.9 H₂:μ = 54.9 The sample Check the conditions to see whether the test statistic will follow a t-distribution. p= B. Ho: μ = 54.9 Ha: μ#54.9 Find the test statistic. E. Ho: μ = 54.9 Ha: μ< 54.9 t= -2.29 (Round to two decimal places as needed.) Find the p-value. is random and the observations are independent. The distribution of the heights is Normally distributed. C. Ho: μ#54.9 Ha: μ = 54.9 (Round to three decimal places as needed.) F. Ho: μ<54.9 Ha: μ = 54.9

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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### Statistical Analysis of Heights in Two Countries In Country A, the population mean height for 10-year-old girls is 54.9 inches with a standard deviation of 1.9 inches. A random sample of 15 10-year-old girls from Country B shows a sample mean height of 53.6 inches and a standard deviation of 2.2 inches. Assuming normally distributed heights, let's complete the following analysis: --- **Objective:** a. **Determine whether the population mean for the height of 10-year-old girls from Country B significantly differs from that of Country A.** **Significance Level:** 0.05 **Hypotheses:** - **Null Hypothesis (\(H_0\)):** \(\mu = 54.9\) - **Alternative Hypothesis (\(H_a\)):** \(\mu \neq 54.9\) (Option B is selected) **Conditions for T-Distribution:** - The sample **is** random. - Observations **are** independent. - The distribution of heights is **Normally distributed**. **Calculating the Test Statistic:** - **Test Statistic (t):** \(-2.29\) (rounded to two decimal places) **Find the p-value:** - **p-value:** (To be rounded to three decimal places as needed with the appropriate statistical software or t-distribution table)
Transcribed Image Text:### Statistical Analysis of Heights in Two Countries In Country A, the population mean height for 10-year-old girls is 54.9 inches with a standard deviation of 1.9 inches. A random sample of 15 10-year-old girls from Country B shows a sample mean height of 53.6 inches and a standard deviation of 2.2 inches. Assuming normally distributed heights, let's complete the following analysis: --- **Objective:** a. **Determine whether the population mean for the height of 10-year-old girls from Country B significantly differs from that of Country A.** **Significance Level:** 0.05 **Hypotheses:** - **Null Hypothesis (\(H_0\)):** \(\mu = 54.9\) - **Alternative Hypothesis (\(H_a\)):** \(\mu \neq 54.9\) (Option B is selected) **Conditions for T-Distribution:** - The sample **is** random. - Observations **are** independent. - The distribution of heights is **Normally distributed**. **Calculating the Test Statistic:** - **Test Statistic (t):** \(-2.29\) (rounded to two decimal places) **Find the p-value:** - **p-value:** (To be rounded to three decimal places as needed with the appropriate statistical software or t-distribution table)
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