A report included the following information on the heights (in.) for non-Hispanic white females.AgeSampleSizeSampleMeanStd. ErrorMean20–3986463.90.0960 and older93662.20.11(a)Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use ?20–39 − ?60 and older.) , Interpret the interval.We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval. We cannot draw a conclusion from the given information.We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval.(b)Let ?1 denote the population mean height for those aged 20–39 and ?2 denote the population mean height for those aged 60 and older. Interpret the hypotheses H0: ?1 − ?2 = 1 and Ha: ?1 − ?2 > 1.The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women.The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is 1 inch higher than for younger women.The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is 1 inch higher than for older women.Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)z=P-value=(c)Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning.Reject H0. The data does not suggest that the difference in the true average heights exceeds 1.Fail to reject H0. The data suggests that the difference in the true average heights exceeds 1. Reject H0. The data suggests that the difference in the true average heights exceeds 1.Fail to reject H0. The data does not suggest that the difference in the true average heights exceeds 1.(d)What hypotheses would be appropriate if ?1 referred to the older age group, ?2 to the younger age group, and you wanted to see if there was compelling evidence for concluding that the population mean height for younger women exceeded that for older women by more than 1 in.?H0: ?1 − ?2 = −1Ha: ?1 − ?2 > −1H0: ?1 − ?2 = −1Ha: ?1 − ?2 < −1 H0: ?1 − ?2 = 1Ha: ?1 − ?2 < 1H0: ?1 − ?2 = 1Ha: ?1 − ?2 > 1You may need to use the appropriate table in the Appendix of Tables to answer this question. (c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning.O Reject Ho. The data does not suggest that the difference in the true average heights exceeds 1.O Fail to reject Ho. The data suggests that the difference in the true average heights exceeds 1.O Reject H. The data suggests that the difference in the true average heights exceeds 1.O Fail to reject Ho. The data does not suggest that the difference in the true average heights exceeds 1.(d) What hypotheses would be appropriate if u, referred to the older age group, µ, to the younger age group, and you wanted to see if there was compelling evidence for concluding that the population meanheight for younger women exceeded that for older women by more than 1 in.?O Ho: H1 - H2 = -1Ha: H1 - H2> -1O Ho: H1 - H2 = -1Hai Hy - H2< -1O Ho: H1- Hz = 1Hai H1 - H2<1O Ho: H1 - H2 = 1Ha: H1 - H2> 1You may need to use the appropriate table in the Appendix of Tables to answer this question. A report included the following information on the heights (in.) for non-Hispanic white females.Sample Sample Std. ErrorМeanAgeSizeMean20-3986463.90.0960 and older93662.20.11(a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use u20-39H60 and older:)Interpret the interval.O We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.O We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval.O We cannot draw a conclusion from the given information.O We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval.(b) Let u, denote the population mean height for those aged 20-39 and µ, denote the population mean height for those aged 60 and older. Interpret the hypotheses H,: µ, - µ, = 1 and H,: µ, - µ, > 1.O The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is morethan 1 inch higher than for younger women.O The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is morethan 1 inch higher than for older women.O The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older womenis 1 inch higher than for younger women.O The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for youngerwomen is 1 inch higher than for older women.Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimalplaces.)Z =P-value =

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A report included the following information on the heights (in.) for non-Hispanic white females. Age Sample Size Sample Mean Std. Error Mean 20–39 864 63.9 0.09 60 and older 936 62.2 0.11 (a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use ?20–39 − ?60 and older.) , Interpret the interval. We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval. We cannot draw a conclusion from the given information.We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval. (b) Let ?1 denote the population mean height for those aged 20–39 and ?2 denote the population mean height for those aged 60 and older. Interpret the hypotheses H0: ?1 − ?2 = 1 and Ha: ?1 − ?2 > 1. The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women.The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is 1 inch higher than for younger women.The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is 1 inch higher than for older women. Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z=P-value= (c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning. Reject H0. The data does not suggest that the difference in the true average heights exceeds 1.Fail to reject H0. The data suggests that the difference in the true average heights exceeds 1. Reject H0. The data suggests that the difference in the true average heights exceeds 1.Fail to reject H0. The data does not suggest that the difference in the true average heights exceeds 1. (d) What hypotheses would be appropriate if ?1 referred to the older age group, ?2 to the younger age group, and you wanted to see if there was compelling evidence for concluding that the population mean height for younger women exceeded that for older women by more than 1 in.? H0: ?1 − ?2 = −1 Ha: ?1 − ?2 > −1H0: ?1 − ?2 = −1 Ha: ?1 − ?2 < −1 H0: ?1 − ?2 = 1 Ha: ?1 − ?2 < 1H0: ?1 − ?2 = 1 Ha: ?1 − ?2 > 1 You may need to use the appropriate table in the Appendix of Tables to answer this question.

A report included the following information on the heights (in.) for non-Hispanic white females. Age Sample Size Sample Mean Std. Error Mean 20–39 864 63.9 0.09 60 and older 936 62.2 0.11 (a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use ?20–39 − ?60 and older.) , Interpret the interval. We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval. We cannot draw a conclusion from the given information.We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval. (b) Let ?1 denote the population mean height for those aged 20–39 and ?2 denote the population mean height for those aged 60 and older. Interpret the hypotheses H0: ?1 − ?2 = 1 and Ha: ?1 − ?2 > 1. The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women.The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is 1 inch higher than for younger women.The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is 1 inch higher than for older women. Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z=P-value= (c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning. Reject H0. The data does not suggest that the difference in the true average heights exceeds 1.Fail to reject H0. The data suggests that the difference in the true average heights exceeds 1. Reject H0. The data suggests that the difference in the true average heights exceeds 1.Fail to reject H0. The data does not suggest that the difference in the true average heights exceeds 1. (d) What hypotheses would be appropriate if ?1 referred to the older age group, ?2 to the younger age group, and you wanted to see if there was compelling evidence for concluding that the population mean height for younger women exceeded that for older women by more than 1 in.? H0: ?1 − ?2 = −1 Ha: ?1 − ?2 > −1H0: ?1 − ?2 = −1 Ha: ?1 − ?2 < −1 H0: ?1 − ?2 = 1 Ha: ?1 − ?2 < 1H0: ?1 − ?2 = 1 Ha: ?1 − ?2 > 1 You may need to use the appropriate table in the Appendix of Tables to answer this question.

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

100%

A report included the following information on the heights (in.) for non-Hispanic white females.

Age	Sample Size	Sample Mean	Std. Error Mean
20–39	864	63.9	0.09
60 and older	936	62.2	0.11

(a)

Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use ?_20–39 − ?_{60 and older}.)

Interpret the interval.

We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval. We cannot draw a conclusion from the given information.We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval.

(b)

Let

?₁

denote the population mean height for those aged 20–39 and ?₂ denote the population mean height for those aged 60 and older. Interpret the hypotheses

H₀: ?₁ − ?₂ = 1

and

H_a: ?₁ − ?₂ > 1.

The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women.The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is 1 inch higher than for younger women.The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is 1 inch higher than for older women.

Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z=P-value=

(c)

Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning.

Reject H₀. The data does not suggest that the difference in the true average heights exceeds 1.Fail to reject H₀. The data suggests that the difference in the true average heights exceeds 1. Reject H₀. The data suggests that the difference in the true average heights exceeds 1.Fail to reject H₀. The data does not suggest that the difference in the true average heights exceeds 1.

(d)

What hypotheses would be appropriate if ?₁ referred to the older age group, ?₂ to the younger age group, and you wanted to see if there was compelling evidence for concluding that the population mean height for younger women exceeded that for older women by more than 1 in.?

H₀: ?₁ − ?₂ = −1
H_a: ?₁ − ?₂ > −1H₀: ?₁ − ?₂ = −1
H_a: ?₁ − ?₂ < −1 H₀: ?₁ − ?₂ = 1
H_a: ?₁ − ?₂ < 1H₀: ?₁ − ?₂ = 1
H_a: ?₁ − ?₂ > 1

You may need to use the appropriate table in the Appendix of Tables to answer this question.

(c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning.
O Reject Ho. The data does not suggest that the difference in the true average heights exceeds 1.
O Fail to reject Ho. The data suggests that the difference in the true average heights exceeds 1.
O Reject H. The data suggests that the difference in the true average heights exceeds 1.
O Fail to reject Ho. The data does not suggest that the difference in the true average heights exceeds 1.
(d) What hypotheses would be appropriate if u, referred to the older age group, µ, to the younger age group, and you wanted to see if there was compelling evidence for concluding that the population mean
height for younger women exceeded that for older women by more than 1 in.?
O Ho: H1 - H2 = -1
Ha: H1 - H2> -1
O Ho: H1 - H2 = -1
Hai Hy - H2< -1
O Ho: H1- Hz = 1
Hai H1 - H2<1
O Ho: H1 - H2 = 1
Ha: H1 - H2> 1
You may need to use the appropriate table in the Appendix of Tables to answer this question.

A report included the following information on the heights (in.) for non-Hispanic white females.
Sample Sample Std. Error
Мean
Age
Size
Mean
20-39
864
63.9
0.09
60 and older
936
62.2
0.11
(a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use u20-39
H60 and older:)
Interpret the interval.
O We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.
O We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval.
O We cannot draw a conclusion from the given information.
O We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval.
(b) Let u, denote the population mean height for those aged 20-39 and µ, denote the population mean height for those aged 60 and older. Interpret the hypotheses H,: µ, - µ, = 1 and H,: µ, - µ, > 1.
O The null hypothesis states that the true mean height for older women is 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women is more
than 1 inch higher than for younger women.
O The null hypothesis states that the true mean height for younger women is 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger women is more
than 1 inch higher than for older women.
O The null hypothesis states that the true mean height for older women is more than 1 inch higher than for younger women. The alternative hypothesis states that the true mean height for older women
is 1 inch higher than for younger women.
O The null hypothesis states that the true mean height for younger women is more than 1 inch higher than for older women. The alternative hypothesis states that the true mean height for younger
women is 1 inch higher than for older women.
Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal
places.)
Z =
P-value =

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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