Question

Last year, during an investigation of the time spent reading emails on a daily basis, researchers found that on Monday the average time was 50 minutes. Office workers claim that with the increased spam and junk mail, this time has now increased. To conduct a test, a sample of 25 employees is selected, with the following results: sample mean = 51.05 minutes and sample standard deviation = 4.42 minutes. Test the hypothesis that the time has increased from last year using a significance of 0.05.

Time reading emails has not increased; p = 0.1233

Time reading emails has increased; p = 0.1233

  

Time reading emails has not increased; p = 0.2465

Time reading emails has increased; p = 0.2465

  

Time reading emails has increased since 51.05 > 50

I know the answer already. PLEASE EXPLAIN!

Answer 1

We will use z test to test difference in mean

H0: The time has increased from last year

x1 = 51.05

x2 = 50

= Z

s1=s2=4.42

n1=n2=25

z = 1.05/ 1.25 = 0.84

From z table We find that the probability of probability of a z-score being 0.84 or less is about 0.02

This is more than significance of 0.05

Hence hypothesis is rejected. Time has not increased significantly.