Question

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 = 0.56	xd = 0.02
sd = 0.81	sd = 0.75
n = 40	n = 40

For purposes of this exercise, 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

α = 0.05.

(Use a statistical computer package to calculate the P-value. Use μ_profile − μ_actual. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

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 μ_profile − μ_actual. Round your answers to two decimal places.)

C) Use the two-sample t test of Section 11.1 to test H₀: μ_m − μ_f = 0 versus H_a: μ_m − μ_f > 0, where μ_m is the mean height difference (profile − actual) for male online daters and μ_f is the mean height difference (profile − actual) for female online daters. (Use α = 0.05.

Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)

t=

df=

P-value=

Answer 1

(a)

Conclusion: There is convincing evidence that, on average, male online daters overstate their height in online dating profiles.

(b)

Interpretation: We are 95% confident that true average difference between the mean online dating profile height and mean actual height for female online daters lies in the above interval.

(c)