samples and that the differences have a distribution that is approximately normal. Use a 0.01 significance level to test the claim that for males, their height is the same as their arm span. Click the icon to view the data from ANSUR II 2012. (Type integers or decimals. Do not round.) Identify the test statistic. \( \mathrm{t}=\square \) (Round to two decimal places as needed.) Identify the P-value. P-value \( =\square \) (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? Since the \( P \)-value is the significance level, the null hypothesis. There sufficient evidence to warrant rejection of the claim that there is no difference between heights and arm spans.
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H₀: μ₁ = μ₂ (The mean height of males is equal to the mean arm span of males) H₁: μ₁ ≠ μ₂ (The mean height of males is not equal to the mean arm span of males) Show more…
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If using the sample data in Data Set 1 "Body Data" in Appendix B for a test of the claim that heights of men and heights of women have different variances, we find that $s=7.48296 \mathrm{cm}$ for women and $s=7.10098 \mathrm{cm}$ for men. a. Find the values of $s_{1}^{2}$ and $s_{2}^{2}$ and express them with appropriate units of measure. b. Identify the null and alternative hypotheses. c. Find the value of the $F$ test statistic and round it to four decimal places. d. The $P$ -value for this test is $0.5225 .$ What do you conclude about the stated claim?
Inferences from Two Samples
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Assume that the paired sample data are simple random samples and tbat the differences bave a distribution that is approximately normal. As part of the National Health and Nutrition Examination Survey, the Department of Health and Human Services obtained self-reported heights and measured heights for males aged $12-16 .$ All measurement are in inches. Listed below are sample results. Construct a $99 \%$ confidence interval estimate of the mean difference between reported heights and measured heights. Interpret the resulting confidence interval, and comment on the implications of whether the confidence interval limits contain $0 .$ $$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|} \hline \text { Reported Height } & 68 & 71 & 63 & 70 & 71 & 60 & 65 & 64 & 54 & 63 & 66 & 72 \\ \hline \text { Measured Height } & 67.9 & 69.9 & 64.9 & 68.3 & 70.3 & 60.6 & 64.5 & 67.0 & 55.6 & 74.2 & 65.0 & 70.8 \\ \hline \end{array}$$
Inference From Two Samples
Two Dependent Samples
Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Assume that a simple random sample is selected from a normally distributed population. Mint Specs Listed below are weights (grams) from a simple random sample of "wheat" pennies (from Data Set 29 "Coin Weights" in Appendix B). U.S. Mint specifications now require a standard deviation of $0.0230 \mathrm{g}$ for weights of pennies. Use a 0.01 significance level to test the claim that wheat pennies are manufactured so that their weights have a standard deviation equal to $0.0230 \mathrm{g}$. Does the Mint specification appear to be met? $$\begin{array}{cccccccc} 2.5024 & 2.5298 & 2.4998 & 2.4823 & 2.5163 & 2.5222 & 2.4900 & 2.4907 & 2.5017 \end{array}$$
Hypothesis Testing
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