Question

Consider a survey of customers who bought a Christmas tree during the holiday season. Respondents were classified as either living in a rural area (population #1) or living in an urban area (population #2). Each respondent was asked whether they purchased a natural tree or an artificial tree. The population proportions in this study are the proportion of persons who bought a natural tree (“success”). (Assume, for this analysis, that the survey was conducted by drawing an SRS from rural dwellers who bought a Christmas tree and an independent SRS from urban dwellers who bought a tree.)

The sample from rural dwellers who bought a tree had a sample size n₁ = 150 and count of “successes” (i.e., number who bought a natural tree) of X₁ = 64.

The sample from urban dwellers who bought a tree had a sample size n₂ = 250 and count of “successes” (i.e., number who bought a natural tree) of X₂ = 80.

Construct the level C = 90% confidence interval for the difference in population means, p₁ - p₂. Also, state the inference about the difference.

Group of answer choices

(0.02, 0.19)   With 90% confidence, the difference in population proportions is greater than zero.

(0.05, 0.11)   With 90% confidence, the difference in population proportions is greater than zero.

(0.04, 0.15)   With 90% confidence, the difference in population proportions is greater than zero.

(0.00, 0.24)   With 90% confidence, the difference in population proportions is not greater than zero.

Answer 1