1. A business consultant wanted to investigate if providing day-care facilities on premises by companies reduces the absentee rate 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. Construct a 98% confidence interval for the difference between the two population means.

b. 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?

c. What are the type 1 error and its probability for the hypothesis test in part b? Explain.