Asoftware company allows their programmers to work from home an average of 20 hours per week. a department of 15 programmers work a mean of 22 hours per week from home with a standard deviation of 5.6 hours. at is their sufficient evidence to conclude a difference? give a 95% confidence interval for the true mean number of hours working from home

The 95% confidence interval would be given by (18.906;25.094)

Since the confidence interval contains the value 20, we don't have enough evidence to conclude a difference.    

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s=5.6 represent the sample standard deviation

n=15 represent the sample size  

2) Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,14)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 95% confidence interval would be given by (18.906;25.094)  

Since the confidence interval contains the value 20, we don't have enough evidence to conclude a difference.  

b) well because you get well