Question

3. A medium size grocery store runs its business 5 days a week for 8 hours each day. The store has two counters and currently Emma and Sophia are working at the counters. The owner of the store wants to study the average time taken to serve a customer by Emma and Sophia. On a randomly selected day, he found that Emma served 50 customers at the counter with a mean time of 4 minutes and a standard deviation of 3 minutes, Sophia served 45 customers with a mean time of 4.3 minutes and a standard deviation of 3.1 minutes. The owner feels the average times of Sophia and Emma are different. He wants to test it at 5% significance level. Assuming equal variances for the time taken by Emma and Sohpia, do an appropriate test to help the owner by answering the following:

   1. State null and alternative hypotheses.

   2. State your decision rule.

   3. Calculate the test statistic.

   4. State your conclusion.

   5. Find the p-value of the test.

Answer 1

Ans:

df=50+45-2=93

critical t value=tinv(0.05,93)=+/-1.986

Decision rule: Reject H0 if t<-1.986 or t>1.986

Pooled standard deviation=sqrt(((50-1)*3^2+(45-1)*3.1^2)/(50+45-2))=3.04772

standard error for difference=3.04772*SQRT((1/50)+(1/45))=0.6262

Test statistic:

t=(4-4.3)/0.6262

t=-0.479

Fail to reject the null hypothesis.

There is not sufficient evidence to conclude that the average times of Sophia and Emma are different.

p-value=tdist(0.479,93,2)=0.6330