Question

Question 3

You are a management consultant who has recently introduced a new procedure to a reception office. The receptionist should do at least 10 minutes of paperwork in each hour. You made a check on 40 random hours of work and found that the mean time spent on paperwork is 8.95 minutes with a standard deviation of 3 minutes. Test to see if the new procedure meets specifications at a 1% level of significance. [18 marks]

Answer 1

Given claim is " receptionist should do at least 10 minutes of paperwork in each hour using new procedure"

Hypothesis:

H0: ( Claim)

H1: ( left tail test)

Level of significance = 0.01

give Sample statistics are

sample size n = 40

sample mean = 8.95 minutes

sample std dev s = 3 minutes.

degrees of freedom df = n - 1 = 40 -1 = 39

rejection criteria:-

critical value = t0.01,39 = -2.426

If the test statistic t39 < -t0.01,39 then reject H0 otherwise fail to reject H0.

Test statistic t = = = -2.214

Since test statistic t39 > -t0.01,39 we fail to reject H0 and there is no statistically sufficient evidence to conclude that mean time spent on paperwork is less than 10 minutes.

we conclude that " receptionist is doing at least 10 minutes of paperwork in each hour using new procedure".