Question

You are interested in opening a Rita’s Ice store in a local mall. The owner of the mall claims that during summer months they get an average of 1,200 people through the mall every day. A sample of 35 days showed an average of 850 people and a sample standard deviation of 60 people. At a 1% level of significance, do you accept or reject the claim?

Answer 1

Solution:

Sample size = n=35

Sample mean ==850

Sample Standard Deviation = s=60

Degrees of freedom =df=n-1=35-1=34

Test Statistic:

Level of significance = α = 1% = 0.01

The test is a two tailed test.

Hence, α/2 = 0.01/2 = 0.005

Critical value:

From t-distribution table, the critical value of ‘t’, having area in the lower tail equal to 0.005 and for df=34 is given by = -2.728

Since the test is a two tailed test, the critical values are: -2.728, 2.728

The value of test statistic (t = -34.51) does not lie between the critical values as defined above. Hence, we reject Ho.

Conclusion: Reject Ho. There is sufficient evidence to reject the claim that during summer months they get an average of 1200 people through the mall every day.