Results of an industry survey in the computer software...

Results of an industry survey in the computer software fields find that the mean number of sick days taken by employees is 9.4 per year with a standard deviation of 2.7 per years. A local computer software company feels its employees take significantly fewer sick days per year. A random sample of 15 employees is selected from the local company and attendance records are reviewed. The following data represent the number of sick days taken by these employees over the past year: 8 10 5 0 6 9 5 15 5 4 3 2 0 4 15

Transcript

00:01 Hey everyone, welcome to numerate.

00:03 We were given a problem here by a survey conducted by industry in the computer software around and given a mean number of six days, 9 .4 and a standard deviation 2 .7.

00:21 We have a sample size 15 with the list of six days given, and we were asked to run a test.

00:31 To see if the sick days is actually less than 9 .4 for the mean at a 0 .05 significance level.

00:42 So from here, we will write the null hypothesis first, and we will do a z test since we are given the population standard deviation.

00:57 Okay, so no hypothesis, since we were looking for fewer than 9 .4, we would do a mule for the average is less than 9 .4.

01:10 And then from here, we would do the alternative hypothesis, where mu is greater than 9 .4, which is the opposite.

01:20 And let's dive into our z test.

01:24 So our z score equation is an x, which is the population mean, minus the mule, which is the sample mean, divided by standard deviation, divided by the zero.

01:33 By square root n.

01:36 And from here, let's define our variables, write out our variable values.

01:42 So this usually is x bar equals.

01:47 So x bar, in this case, what the population mean.

01:50 So it's going to be 9 .4.

01:55 And in meal, mu will equal.

02:00 So we had to sum up all the values in the list and it divided by the number, the number would be 15.

02:10 So x divided by the number.

02:22 The number is 15, so let's just plug you down for 15...