A paper describes an investigation in which 40 men and 40 women with online dating profiles agreed to participate in a study. Each participant's height (in inches) was measured and the actual height was compared to the height given in that person's online profile. The differences between the online profile height and the actual height (profile − actual) were used to compute the values in the accompanying table. Men Women xd = 0.59 xd = 0.01 sd = 0.81 sd = 0.75 n = 40 n = 40 You can assume it is reasonable to regard the two samples in this study as being representative of male online daters and female online daters. (Although the authors of the paper believed that their samples were representative of these populations, participants were volunteers recruited through newspaper advertisements, so we should be a bit hesitant to generalize results to all online daters.) (a) Use the paired t test to determine if there is convincing evidence that, on average, male online daters overstate their height in online dating profiles. Use ? = 0.05. (Use ?d = ?profile − ?actual.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Reject H0. We do not have convincing evidence that male online daters overstate their height in online dating profiles.Fail to reject H0. We have convincing evidence that male online daters overstate their height in online dating profiles. Fail to reject H0. We do not have convincing evidence that male online daters understate their height in online dating profiles.Reject H0. We have convincing evidence that male online daters overstate their height in online dating profiles. (b) Construct and interpret a 95% confidence interval for the difference between the mean online dating profile height and mean actual height for female online daters. (Use technology to calculate the critical value. Use ?d = ?profile − ?actual. Round your answers to three decimal places.) , inches Interpret the interval. We are 95% confident that the true mean online dating profile height is between these two values.There is a 95% chance that the true mean online dating profile height is directly in the middle of these two values. We are 95% confident that the true mean actual height for female online daters is between these two values.We are 95% confident that the true difference in mean online dating profile height and mean actual height for female online daters is between these two values.There is a 95% chance that the true difference in mean online dating profile height and mean actual height for female online daters is directly in the middle of these two values. (c) Use the two-sample t test of Section 11.1 to test H0: ?m − ?f = 0 versus Ha: ?m − ?f > 0, where ?m is the mean height difference (profile − actual) for male online daters and ?f is the mean height difference (profile − actual) for female online daters. (Use ? = 0.05.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. (Round your answer down to the nearest whole number.) df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Reject H0. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.Reject H0. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters. Fail to reject H0. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.Fail to reject H0. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters.

A paper describes an investigation in which 40 men and 40 women with online dating profiles agreed to participate in a study. Each participant's height (in inches) was measured and the actual height was compared to the height given in that person's online profile. The differences between the online profile height and the actual height (profile − actual) were used to compute the values in the accompanying table. Men Women xd = 0.59 xd = 0.01 sd = 0.81 sd = 0.75 n = 40 n = 40 You can assume it is reasonable to regard the two samples in this study as being representative of male online daters and female online daters. (Although the authors of the paper believed that their samples were representative of these populations, participants were volunteers recruited through newspaper advertisements, so we should be a bit hesitant to generalize results to all online daters.) (a) Use the paired t test to determine if there is convincing evidence that, on average, male online daters overstate their height in online dating profiles. Use ? = 0.05. (Use ?d = ?profile − ?actual.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Reject H0. We do not have convincing evidence that male online daters overstate their height in online dating profiles.Fail to reject H0. We have convincing evidence that male online daters overstate their height in online dating profiles. Fail to reject H0. We do not have convincing evidence that male online daters understate their height in online dating profiles.Reject H0. We have convincing evidence that male online daters overstate their height in online dating profiles. (b) Construct and interpret a 95% confidence interval for the difference between the mean online dating profile height and mean actual height for female online daters. (Use technology to calculate the critical value. Use ?d = ?profile − ?actual. Round your answers to three decimal places.) , inches Interpret the interval. We are 95% confident that the true mean online dating profile height is between these two values.There is a 95% chance that the true mean online dating profile height is directly in the middle of these two values. We are 95% confident that the true mean actual height for female online daters is between these two values.We are 95% confident that the true difference in mean online dating profile height and mean actual height for female online daters is between these two values.There is a 95% chance that the true difference in mean online dating profile height and mean actual height for female online daters is directly in the middle of these two values. (c) Use the two-sample t test of Section 11.1 to test H0: ?m − ?f = 0 versus Ha: ?m − ?f > 0, where ?m is the mean height difference (profile − actual) for male online daters and ?f is the mean height difference (profile − actual) for female online daters. (Use ? = 0.05.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. (Round your answer down to the nearest whole number.) df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value = State your conclusion. Reject H0. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.Reject H0. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters. Fail to reject H0. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.Fail to reject H0. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters.

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

Men	Women
x_d = 0.59	x_d = 0.01
s_d = 0.81	s_d = 0.75
n = 40	n = 40

You can assume it is reasonable to regard the two samples in this study as being representative of male online daters and female online daters. (Although the authors of the paper believed that their samples were representative of these populations, participants were volunteers recruited through newspaper advertisements, so we should be a bit hesitant to generalize results to all online daters.)

(a)

Use the paired t test to determine if there is convincing evidence that, on average, male online daters overstate their height in online dating profiles. Use

? = 0.05.

(Use ?_d = ?_profile − ?_actual.)

Find the test statistic. (Round your answer to two decimal places.)

t =

Find the df.

df =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

State your conclusion.

Reject H₀. We do not have convincing evidence that male online daters overstate their height in online dating profiles.Fail to reject H₀. We have convincing evidence that male online daters overstate their height in online dating profiles. Fail to reject H₀. We do not have convincing evidence that male online daters understate their height in online dating profiles.Reject H₀. We have convincing evidence that male online daters overstate their height in online dating profiles.

(b)

Construct and interpret a 95% confidence interval for the difference between the mean online dating profile height and mean actual height for female online daters. (Use technology to calculate the critical value. Use ?_d = ?_profile − ?_actual. Round your answers to three decimal places.)

inches

Interpret the interval.

We are 95% confident that the true mean online dating profile height is between these two values.There is a 95% chance that the true mean online dating profile height is directly in the middle of these two values. We are 95% confident that the true mean actual height for female online daters is between these two values.We are 95% confident that the true difference in mean online dating profile height and mean actual height for female online daters is between these two values.There is a 95% chance that the true difference in mean online dating profile height and mean actual height for female online daters is directly in the middle of these two values.

(c)

Use the two-sample t test of Section 11.1 to test

H₀: ?_m − ?_f = 0 versus H_a: ?_m − ?_f > 0,

where

?_m

is the mean height difference (profile − actual) for male online daters and

?_f

is the mean height difference (profile − actual) for female online daters. (Use

? = 0.05.)

Find the test statistic. (Round your answer to two decimal places.)

t =

Find the df. (Round your answer down to the nearest whole number.)

df =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

State your conclusion.

Reject H₀. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.Reject H₀. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters. Fail to reject H₀. We have convincing evidence that mean height difference for male online daters is greater than mean height difference for female online daters.Fail to reject H₀. We do not have evidence that mean height difference for male online daters is greater than mean height difference for female online daters.

(d)

Explain why a paired t test was used in part (a) but a two-sample t test was used in part (c).

Part (a) used a paired t test because the profile and actual heights were connected, while part (b) used a two-sample t test because the males and females were from independent samples.Part (a) used a paired t test because there were a different number of profile and actual heights, while part (b) used a two-sample t test because there were the same number of males and females. Part (a) used a paired t test because the profile and actual heights were from independent samples, while part (b) used a two-sample t test because the males and females were connected.Part (a) used a paired t test because there were the same number of profile and actual heights, while part (b) used a two-sample t test because there were a different number of males and females.

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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