# 1. Consider this hypothesis test: H0: p1 - p2 = < 0

aH_{a}: p_{1} - p_{2} > 0

Here p_{1} is the population proportion of "yes" of Population 1 and p_{2} is the population proportion of "yes" of Population 2. Use the statistics data from a simple random sample of each of the two populations to complete the following: (**8 marks**)

**Population 1**

**Population 2**

Sample Size (n)

500

700

Number of "yes"

400

560

Draw a diagram for the problem marking in all the relevant values.

a. Compute the test statistic z

Mark in the Z value based on a =0.05. Note this is a 2-tailed test.

b. Should H_{0} be rejected?

c. Also, What is the p-value?

Use the p-value and a level of significance of 0.05 to justify your answer.

d. Use the above data to construct a 90% confidence interval for p_{1} - p_{2}