evidence that the true mean IQ for girls who want to be engineers differs from the mean IQ of
all girls in this age range.example: A company president believes that there are more absences on Monday than on other
days of the week. The company has 45 workers. The following table gives the number of
worker absences on Mondays and Wednesdays for a random sample of 8-weeks from the past
two years. Do the data provide evidence that there are more absences on Mondays?
solution: Because the data are paired on a weekly basis, the data we use for this problem are the
difference between the days of the week for each of the 8 weeks. Adding a row to the table that
gives the differences (absences on Monday minus absences on Wednesday), we have:
I . Let μ (^) d = the true mean difference between number of absences on Monday and absences on
Wednesday.
H 0 : μ (^) d = 0(or H 0 : μ (^) d ≤ 0).
H (^) A : μ (^) d > 0.
II . We will use a one-sample t -test for the difference scores.
Conditions:
A boxplot of the data shows no significant departures from normality (no outliers or severe
skewness). Also, we are told that the 8-weeks are randomly selected.