Do men have a higher body temperature than women? Test the indicated claim about the means of two populations. Assume that the two samples are randomly selected, independent, the population standard deviations are not know and not considered equal. The table shows results from a study of body temperatures of men and women. At the 0.05 significance level, test the claim that men have a higher body temperature than women. Men Women n1 = 13 n2 = 16 xˉx̄1 = 97 °F xˉx̄2 = 95.17 °F s1 = 0.26 °F s2 = 0.57 °F What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: Select an answer x̄₂ μ₁ p p₂ μ₂ μ μ(men) p̂₁ x̄₁ σ₁² p₁ s₁² ? > < ≥ ≠ ≤ = Select an answer p̂₁ p₁ μ μ₁ p x̄₁ μ₂ s₁² x̄₂ μ(women) σ₁² p₂ H1: Select an answer σ₂² μ p̂₂ p₁ p p₂ x̄₁ μ(men) x̄₂ μ₂ μ₁ s₂² ? = ≤ > < ≥ ≠ Select an answer s₁² x̄₁ μ₂ μ p̂₁ x̄₂ σ₁² μ(women) p₁ p p₂ μ₁ Original Claim = Select an answer H₀ H₁ df = Based on the hypotheses, find the following: Test Statistic = (Round to three decimal places.) Critical value(s) = (Round to three decimal places.) Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the t-score(s). Shade: Left of a valueRight of a valueBetween two values2 regions. Click and drag the arrows to adjust the values. -1.5 Decision: Select an answer Accept the null hypothesis Accept the alternative hypothesis Reject the null hypothesis Fail to reject the null hypothesis . Conclusion: Select an answer There is sufficient evidence to warrant rejection of There is not sufficient evidence to warrant rejection of The sample data supports There is not enough evidence to support the claim that men have a higher body temperature than women.

Do men have a higher body temperature than women? Test the indicated claim about the means of two populations. Assume that the two samples are randomly selected, independent, the population standard deviations are not know and not considered equal. The table shows results from a study of body temperatures of men and women. At the 0.05 significance level, test the claim that men have a higher body temperature than women. Men Women n1 = 13 n2 = 16 xˉx̄1 = 97 °F xˉx̄2 = 95.17 °F s1 = 0.26 °F s2 = 0.57 °F What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: Select an answer x̄₂ μ₁ p p₂ μ₂ μ μ(men) p̂₁ x̄₁ σ₁² p₁ s₁² ? > < ≥ ≠ ≤ = Select an answer p̂₁ p₁ μ μ₁ p x̄₁ μ₂ s₁² x̄₂ μ(women) σ₁² p₂ H1: Select an answer σ₂² μ p̂₂ p₁ p p₂ x̄₁ μ(men) x̄₂ μ₂ μ₁ s₂² ? = ≤ > < ≥ ≠ Select an answer s₁² x̄₁ μ₂ μ p̂₁ x̄₂ σ₁² μ(women) p₁ p p₂ μ₁ Original Claim = Select an answer H₀ H₁ df = Based on the hypotheses, find the following: Test Statistic = (Round to three decimal places.) Critical value(s) = (Round to three decimal places.) Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the t-score(s). Shade: Left of a valueRight of a valueBetween two values2 regions. Click and drag the arrows to adjust the values. -1.5 Decision: Select an answer Accept the null hypothesis Accept the alternative hypothesis Reject the null hypothesis Fail to reject the null hypothesis . Conclusion: Select an answer There is sufficient evidence to warrant rejection of There is not sufficient evidence to warrant rejection of The sample data supports There is not enough evidence to support the claim that men have a higher body temperature than women.

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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Question

Do men have a higher body temperature than women?

Test the indicated claim about the means of two populations. Assume that the two samples are randomly selected, independent, the population standard deviations are not know and not considered equal. The table shows results from a study of body temperatures of men and women. At the 0.05 significance level, test the claim that men have a higher body temperature than women.

Men	Women
n₁ = 13	n₂ = 16
xˉx̄₁ = 97 °F	xˉx̄₂ = 95.17 °F
s₁ = 0.26 °F	s₂ = 0.57 °F

What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)

H₀: Select an answer x̄₂ μ₁ p p₂ μ₂ μ μ(men) p̂₁ x̄₁ σ₁² p₁ s₁² ? > < ≥ ≠ ≤ = Select an answer p̂₁ p₁ μ μ₁ p x̄₁ μ₂ s₁² x̄₂ μ(women) σ₁² p₂

H₁: Select an answer σ₂² μ p̂₂ p₁ p p₂ x̄₁ μ(men) x̄₂ μ₂ μ₁ s₂² ? = ≤ > < ≥ ≠ Select an answer s₁² x̄₁ μ₂ μ p̂₁ x̄₂ σ₁² μ(women) p₁ p p₂ μ₁

Original Claim = Select an answer H₀ H₁

df =

Based on the hypotheses, find the following:

Test Statistic = (Round to three decimal places.)

Critical value(s) = (Round to three decimal places.)

Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the t-score(s).

Shade: Left of a valueRight of a valueBetween two values2 regions. Click and drag the arrows to adjust the values.

-1.5

Decision: Select an answer Accept the null hypothesis Accept the alternative hypothesis Reject the null hypothesis Fail to reject the null hypothesis .

Conclusion: Select an answer There is sufficient evidence to warrant rejection of There is not sufficient evidence to warrant rejection of The sample data supports There is not enough evidence to support the claim that men have a higher body temperature than women.

Expert Solution

Step 1

Given:

$n_{1} = 13 n_{2} = 16 {\bar{x}}_{1} = 97 {\bar{x}}_{2} = 95.17 s_{1} = 0.26 s_{2} = 0.57 α = 0.05$

The correct test hypothesis are,

H₀: μ₁- μ₂ =0

H₁: μ₁- μ₂ > 0

This is an upper tailed test.

We reject the null hypothesis if t-value > t-critical value.

Step 2

The test statistic is computed as,

$t = \frac{{\bar{x}}_{1} - {\bar{x}}_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}}} = \frac{97 - 95.17}{\sqrt{\frac{0 . 26^{2}}{13} + \frac{0 . 57^{2}}{16}}} = 11.4585$

$d f = \frac{{(\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}})}^{2}}{\frac{{(\frac{s_{1}^{2}}{n_{1}})}^{2}}{n_{1} - 1} + \frac{{(\frac{s_{2}^{2}}{n_{1}})}^{2}}{n_{2} - 1}} = \frac{{(\frac{0 . 26^{2}}{13} + \frac{0 . 57^{2}}{16})}^{2}}{\frac{{(\frac{0 . 26^{2}}{13})}^{2}}{13 - 1} + \frac{{(\frac{0 . 57^{2}}{16})}^{2}}{16 - 1}} = 21.8731$

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