1. A researcher wants to test the hypothesis that the mean

height of male students in a university is 175 cm. He

collects a random sample of 100 male students and

measures their heights. He finds that the sample mean is

173 cm and the sample standard deviation is 10 cm. What

is the p-value for his hypothesis test?

a) 0.1587

b) 0.3174

c) 0.8413

d) 0.6826

*Answer: a) 0.1587*

Rationale: The p-value is the probability of obtaining a

sample mean as extreme or more extreme than the

observed one, assuming that the null hypothesis is true. The

null hypothesis is that the population mean is 175 cm, and

the alternative hypothesis is that it is not. The test statistic

is z = (173 - 175) / (10 / sqrt(100)) = -2. The p-value is P(Z

< -2) = 0.1587.

2. A company wants to compare the effectiveness of two

different marketing strategies for its new product. It

randomly assigns 500 customers to receive either strategy

A or strategy B and records their purchase decisions. It

finds that 120 customers who received strategy A bought

the product, while 150 customers who received strategy B

bought the product. What is the appropriate statistical test

to analyze this data?