1. [10 points) A business consultant wanted to investigate if providing day-care facilities on premises
by companies reduces the absentee rate of working
mothers with children under six years old. She took a
sample of 45 such mothers from companies that provide
day-care facilities on premises. These mothers missed
an average of 6.4 days from work last year with a
standard deviation of 1.20 days. Another sample of 50
such mothers taken from companies that do not provide
day-care facilities on premises showed that these
mothers missed an average of 9.3 days last year with a
standard deviation of 1.85 days.
a. Using a 2.5% significance level, can you conclude that
the mean number of days missed per year by mothers
working for companies that provide day-care facilities
on premises is less than the mean number of days missed
per year by mothers working for companies that do not
provide day-care facilities on premises?
b. Describe the Type 1 error in the context of the
problem and its probability for the hypothesis test.