A 20-minute consumer survey mailed to 350 adults aged 25-34 included a $5 Starbucks gift certificate. The same survey was mailed to 350 adults aged 25-34 without the gift certificate. There were 50 responses from the first group and 29 from the second group. From 95% confidence interval for the difference of proportion. Does it include zero?

-0.0133 < p < 0.10667

- It does include zero

Step-by-step explanation:

Given:

- The number of responses with certificate p_1 = 50

- The number of responses without certificate p_2 = 29

- Total sample size n = 350 adults

Find:

From 95% confidence interval for the difference of proportion. Does it include zero?

Solution:

- Formulate the proportion of people with and without certificate:

p_hat with certificate = p_1 / n = 50/350 = 1/7

p_hat w/o certificate = p_2 / n = 29/350 = 0.082857

- Next compute the critical value of 95% confidence interval:

Z_0.05 = 1.96

- The confidence interval is:

E = 1.96*sqrt [ (1/7) * (1-1/7) / 350 + (0.082857) * (1 - 0.082857) / 350 ]

E = 0.04667

C. I : E - (P_hat difference) < p < E + (P_hat difference)

0.04667 - (0.06) < p < 0.04667 + (0.06)

-0.0133 < p < 0.10667

- It does include zero