A paper describes an investigation in which 40 men and 40 womenwith online dating profiles agreed to participate in a study. Eachparticipant's height (in inches)was measured and the actual heightwas compared to the height given in that person's online profile.The differences between the online profile height and the actualheight (profile − actual) were used to compute the values in theaccompanying 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 regardthe two samples in this study as being representative of maleonline daters and female online daters. (Although the authors ofthe paper believed that their samples were representative of thesepopulations, participants were volunteers recruited throughnewspaper advertisements, so we should be a bit hesitant togeneralize results to all online daters.)
Use the paired t test to determine if there isconvincing evidence that, on average, male online daters overstatetheir height in online dating profiles. Use
α = 0.05.
(Use a statistical computer package to calculate theP-value. Use μd = μprofile− μactual. Round your test statistic to two decimalplaces, your df down to the nearest whole number, and yourP-value to three decimal places.)
t=
df =
P-value =
(b)
Construct and interpret a 95% confidence interval for thedifference between the mean online dating profile height and meanactual height for female online daters. (Use μd= μprofile − μactual. Round your answers totwo decimal places.)
____to___ inches
(c)
Use the two-sample t test of Section 11.1 to testH0: μm − μf = 0 versusHa: μm − μf > 0, whereμm is the mean height difference (profile − actual) formale online daters and μf is the mean height difference(profile − actual) for female online daters. (Use α = 0.05. Use astatistical computer package to calculate the P-value.Round your test statistic to two decimal places, your df down tothe nearest whole number, and your P-value to threedecimal places.)
t=
df =
P-value =
