A business manager is interested in the amount of overtime employees at their company complete over the year. The manager would like to test the claim that the average amount of overtime employees from the human resources department complete is less than employees from the management department. They collected a random sample of human resources employees and management employees and recorded the amount of overtime completed in the past year. The summary statistics (in hours) are shown in the following table.

Assume that the times are normally distributed and that the population variances are not equal. At the 0.025 level of significance, is there sufficient evidence that the average amount of overtime employees from the human resources department complete over the year is less than employees from the management department?

Let 1 represent the mean overtime for human resources employees and 2 represent the mean overtime for management employees.

Overtime for human resources (in hours)	Overtime for management (in hours)
x1=210	x2=220
s1=14	s2=19
n1=10	n2=10

Using the table below, find the degrees of freedom and the approximate range for the p-value given thatthe test statistic is 1.61. Enter the p-values in order from smallest to largest.

Probability	0.10	0.05	0.025	0.01	0.005
Degrees of Freedom
7	1.415	1.895	2.365	2.998	3.499
8	1.397	1.860	2.306	2.896	3.355
9	1.383	1.833	2.262	2.821	3.250
10	1.372	1.812	2.228	2.764	3.169
11	1.363	1.796	2.201	2.718	3.106
12	1.356	1.782	2.179	2.681	3.055
13	1.350	1.771	2.160	2.650	3.012

Provide your answer below:

degrees of freedom =

p-value is between and .