An association of Christmas tree growers in Indiana sponsored a sample survey of households to help improve the marketing of Christmas trees

Question

Of 421 households that do display a Christmas tree, 160 lived in rural areas and 261 were urban residents. The tree growers want to know if there is a difference in preference for natural trees versus artificial trees between urban and rural households. The data below shows the number of households from urban and rural areas that have natural trees.

Population	n	# with Natural trees
#1 Rural	160	64
#2 Urban	261	89

Use an appropriate statistical procedure to answer the tree growers’ question.

Answer 1

We will use the 2-proportional z-test.

H_o: P₁ = P₂

H_A: P₁ ≠ P₂

P₁ = 64/160 = 0.40 (sample proportion for rural households who prefer a natural tree)

P₂ = 89/261 = 0.341 (sample proportion for urban households who prefer a natural tree)

P-pooled = (64 + 89) / (160 + 261) = 153/421 = 0.363 (sample proportion for all households who prefer a natural tree)

z = (0.40 - 0.341) / √(0.363)(0.637)[(1/160)+(1/261)] = 0.059/0.0483 = 1.22

Look at the z-critical value for the 95% confidence level. The z-critical is 1.96.

Since 1.22 < 1.96, we fail to reject the null hypothesis. There is not sufficient evidence to show the difference in preference for natural trees vs. artificial trees between urban and rural households.