### Statistical Testing: Heights of Female Students#### BackgroundHeights of females follow a normal distribution with a mean (μ) of 64.5 inches in the United States.#### Problem Statement(a) A sample of 15 female students at UNC has a mean height of 65.73 inches and a sample standard deviation of 2.5 inches. Is this strong evidence that the average height of female students at UNC is higher than the national average?### Hypothesis Testing Steps:#### I. State the HypothesisSelect the appropriate hypothesis:- $ H_0: \mu = 64.5, H_a: \mu \neq 64.5 $- $ H_0: \mu = 64.5, H_a: \mu < 64.5 $- $ H_0: \mu = 64.5, H_a: \mu > 64.5 $#### II. Compute the Test StatisticCalculate the test statistic (t) and provide the answer to two decimal places:\[ t = \] [Calculated Value]#### III. Compute the p-ValueDetermine the p-value to four decimal places:\[ \text{p-value} = \] [Calculated Value]#### IV. State Your Conclusion at the 5% Significance LevelBased on your analysis, decide whether to reject or fail to reject the null hypothesis:- $ \bigcirc $ Reject $ H_0 $- $ \bigcirc $ Fail to reject $ H_0 $### Explanation of Concepts:1. **Hypothesis Selection**: Choose the hypothesis based on whether you need to prove the average height is different or greater than the national average.2. **Test Statistic**: The t-score measures how far the sample mean deviates from the population mean in units of standard error.3. **p-Value**: The probability that the observed results occurred by chance. A p-value below 0.05 typically means you reject the null hypothesis.4. **Conclusion**: At a 5% significance level, decide if the evidence is strong enough to claim the average height at UNC is greater than the national average.

We have given that Sample size n=15 ,mu=64.5 ,xbar=65.73 and s=2.5 ,alpha=0.05

Heights of females follow a normal distribution with mean 64.5 inches in the United States. (a) You take a sample of 15 female students at UNC and observe the sample mean of heights to be 65.73 inches and the sample standard deviation to be 2.5 inches. Is this strong enough evidence that the average height of female students at UNC is higher than national average? (I) State the hypothesis. Ο H0: μ=64.5, Ha: μ+ 64.5 Ο Ho: μΕ64.5, Ha: μ< 64.5 Ο Hρ: μ-64.5, Ha: μ > 64.5 (II) Compute the test statistic. (Answer to two decimal places) t = (III) Compute the p-value. (Answer to four decimals) (IV) State your conclusion at the 5% significance level. O Reject Ho O Fail to reject Ho

Heights of females follow a normal distribution with mean 64.5 inches in the United States. (a) You take a sample of 15 female students at UNC and observe the sample mean of heights to be 65.73 inches and the sample standard deviation to be 2.5 inches. Is this strong enough evidence that the average height of female students at UNC is higher than national average? (I) State the hypothesis. Ο H0: μ=64.5, Ha: μ+ 64.5 Ο Ho: μΕ64.5, Ha: μ< 64.5 Ο Hρ: μ-64.5, Ha: μ > 64.5 (II) Compute the test statistic. (Answer to two decimal places) t = (III) Compute the p-value. (Answer to four decimals) (IV) State your conclusion at the 5% significance level. O Reject Ho O Fail to reject Ho

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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