A large company is considering a policy of flextime. in which employees can choose their own work schedules within broad limits. The company is interested to determine whether this policy would reduce the number of sick days taken. They chose two simple random samples of 100 employees each. The employees in one sample were allowed to choose their own schedules. The other sample was a control group. Employees in that sample were required to come to work according to a schedule set by management. At the end of one year, the employees in the flextime group had a sample mean of 4. 7 days missed, with a sample standard deviation of 3.1 days. The employees in the control group had a sample mean of 4. 9 days missed, with a sample standard deviation of 3.9 days. Perform a hypothesis test to measure the strength of the evidence that the mean number of days missed is less in the flextime group. State the null and alternate hypotheses, find the P-value, and state your conclusion. Use the α = 0.01 level of significance.