Question

Best Buy offers warranty packages on all the new televisions it sells nationwide.  60% of all customers who purchase new televisions purchase the warranty as well.  I would like to know if the same average of people in Michigan purchase the warranty, so I decide to take a survey of 100 Best Buy customers from local stores.

1.      What proportion of customers would you expect to purchase the warranty?

2.      What is the Standard Deviation of the sample proportion?

3.      What shape would you expect the sampling distribution of the proportion to have?

4.      Would you be surprised to find out in the sampling that only 30% of customers would purchase the warranty? Explain

Answer 1

1.

Proportion of customers who purchase the warranty, p = 0.6

Expected proportion of customers to purchase the warranty = 0.6 * 100 = 60

2.

Standard Deviation of the sample proportion, s  =

3.

The sampling distribution of the proportion is almost Normal distribution if np(1-p) > 10

100 * 0.6 * (1-0.6) = 24 > 10

Thus, sampling distribution of the proportion is almost Normal distribution and the shape would be symmetrical bell curve.

4.

Observed sample proportion, pnew = 0.3

Test statistic, z = (pnew - p) / s = (0.3 - 0.6)/ 0.04898979 = -6.12

P(z = -6.12) = 0   

So, the probability of 30% of customers to purchase the warranty is 0 and we will definitely surprised to find out in the sampling that only 30% of customers would purchase the warranty.