Question

Use a 5% significance level for all hypothesis tests (α=.05) unless otherwise noted. Give conclusions as complete sentences. This is considered an ‘open book’ test so you may use the text, StatCrunch, any notes you have, or lecture videos. You should not consult other individuals.

1. A marketing firm was hired by the Acme Company to determine if internet advertising for the company was equally effective in reaching men and women. They sampled 675 men and 703 women and found that 297 of the men and 246 of the women had seen ads for the Acme Company over the previous month.

a) Which test should be performed?

b) State the null and alternative hypotheses.

c) Use StatCrunch to find the test statistic and the p-value.

d) Do you reject or fail to reject the null hypotheses?

e) State the conclusion in a complete sentence.

Answer 1

Question 1

Here we will count men as population 1 and women as population 2

(a) Here we will perform z test for difference in two population proportions.

(b) Null Hypothesis : H0 : p1 = p2

Alternative Hypothesis : Ha : p1 p2

(b) Here sample proportion of population 1 = = 297/675 = 0.44

sample proportion of population 2 = = 246/703 = 0.35

pooled proportion = p = (x1 + x2)/(n1 + n2) = (297 + 246)/(675 + 703) = 0.394

standard error of proportion in differences = sep = sqrt [0.394 * (1-0.394) * (1/675 + 1/703] = 0.02633

Test statistic

z = (0.44 - 0.35)/0.02633 = 3.42

p - value = 2 * P(Z > 3.42) = 0.0006

(d) Here p - value < 0.05 so we would reject the null hypothesis.

(e) Here we conclude that there is significant difference between internet advertising for the company was equally effective in reaching men and women.