Question

The owners of a shopping mall had studied the shopping habits of their customers. Historical data

showed that the mean time spent by shoppers in the mall was 60 minutes. The owners improved

the mall and wished the improvement would cause shoppers to spend more time in the mall. A

random sample of 50 shoppers is selected, the average time spent by these shoppers in the mall is

62 minutes with a standard deviation of 5 minutes.

(a) Use p-value approach, is there evidence to suggest that the improvement has caused

shoppers to spend more time in the mall at 5% level of significance?

(b) Explain why the sampling distribution of sample mean follow the normal distribution in this

case.

Answer 1

a)

n= 50, s= 5, = 62, =60

Ho: =60

Ha: > 60

Calculate test statistics

t= 2.828

test statistics= 2.828

Now calculate P-value for right tailed test with df= n-1= 50-1= 49

We get

P-value=0.0034

now rule is

Reject Ho if (p-value) ()

Here (P-value=0.0034) < (=0.05)

Hence ,

Reject null hypothesis.

Therefore there is enough evidence to suggest that the improvement has caused shoppers to spend more time in the mall at 5% level of significanc

b)

according to central limit theorem, for samples of size 30 or more, the sample mean is approximately normally distributed.

Here sample size is 50. Which is greater than 30.

Hence sampling distribution is approximately normal.