Question

Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all its credit card customers. This promotion will be considered a success if more than of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of credit card customers.

Required:
a. Develop hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national.
b. The file Eagle contains the sample data. Develop a point estimate of the population proportion.
c. Use α= 0.05 to conduct your hypothesis test. Should Eagle go national with the promotion?

Answer 1

Answer:

Step-by-step explanation:

Assuming that:

the promotion will be considered to be a  success if more than 10% use the coupons received.

and coupons are sent to 100 credit card customers.

Then, the null hypothesis and alternative hypothesis is:

$\mathbf{H_o:p\le 0.10} \\ \\ \mathbf{H_a:p> 0.10}$

sample size n = 100

Using the eagle file data;

the no of people in the sample who use the coupon = 13

then,

$\hat p = \dfrac{x}{n}$

$\hat p = \dfrac{13}{100}$

$\hat p = 0.13$

Test statistics can be computed as:

$Z = \dfrac{\hat p - p }{\sqrt{\dfrac{p(1-p)}{n}}}$

$Z = \dfrac{0.13 - 0.10 }{\sqrt{\dfrac{0.10(1-0.10)}{100}}}$

$Z = \dfrac{0.03 }{\sqrt{\dfrac{0.09}{100}}}$

$Z = \dfrac{0.03 }{\sqrt{0.0009}}$

$Z = \dfrac{0.03 }{0.03}$

$Z = 1$

$P-value = P(Z > 1) \\ \\ P-value = 1 - P(Z < 1 ) \\ \\ P-value = 1 - 0.8413 \\ \\ P-value = 0.1587$

At ∝ = 0.05

Since, P-value is greater than ∝, then we fail to reject $\mathbf{H_o}$.

Therefore, Eagle should not go with the promotion; a larger sample should be taken.