-Question:Consumers’ use of discount coupons. In 1894, druggist Asa Candler began distributing handwritten tickets to his customers for free glasses of Coca-Cola at his soda fountain. That was the genesis of the discount coupon. In 1975, it was estimated that 65% of U.S. consumers regularly used discount coupons when shopping. In a more recent consumer survey, 81% said they regularly redeem coupons (NCH Marketing Services 2015 Consumer Survey). Assume the recent survey consisted of a random sample of 1,000 shoppers.

a. Does the survey provide sufficient evidence that the percentage of shoppers using cents-off coupons exceeds 65%? Test using α = 0.05.

b. Is the sample size large enough to use the inferential procedures presented in this section? Explain.

c. Find the observed significance level for the test you conducted in part a and interpret its value.

A random sample of size n = 1000 shoppers is surveyed. The sample proportion of shoppers that uses cents-off coupons is .

The researcher wants to test the claim that the percentage of shoppers using cents-off coupons exceeds 65%.

The null and alternative hypotheses are:

H₀ : p = 0.65AgainstH_a: p > 0.65

a.

The test statistic is:

The test statistic is z = 10.596.

The z-critical value at a 5% significance level for the right-tailed test using the z-table is 1.65.

Since the test statistic exceeds the critical value, reject the null hypothesis.

Therefore, there is enough evidence that the percentage of shoppers using cents-off coupons exceeds 65%.

(b)

The minimum sample size required to use the z-test for the significance of the population proportion is obtained by the following conditions:

and.

Here,

and

Since both conditions are satisfied, the sample size is large enough to use the inferential procedures.

(c)

Referring to part a., the test statistic is z = 10.596. The significance level is α = 0.05.

The observed significance level or the p-value for the right-tailed test is obtained as follows:

From the z-table, the p-value is approximately zero.

Therefore, the observed significance level is 0.00. It is the probability of getting the test statistic more than the observed value.