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

men in a certain population is 175 cm. He collects a random sample

of 100 men and measures their heights. The sample mean is 173

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

appropriate test statistic for this hypothesis test?

A) t = -1.96

B) t = -2

C) z = -1.96

D) z = -2

Answer: B) t = -2

Rationale: Since the population standard deviation is unknown, a ttest is appropriate. The test statistic is calculated as t = (x̄ - μ) / (s /

√n), where x̄ is the sample mean, μ is the population mean, s is the

sample standard deviation, and n is the sample size. Plugging in the

given values, we get t = (173 - 175) / (10 / √100) = -2.

2. A survey asks 500 people to rate their satisfaction with a new

product on a scale from 1 (very dissatisfied) to 5 (very satisfied). The

results are summarized in the following table:

| Rating | Frequency |

|--------|-----------|

| 1 | 50 |

| 2 | 75 |

| 3 | 150 |

| 4 | 125 |

| 5 | 100 |

What is the mean rating of the product?

A) 3

B) 3.1

C) 3.2

D) 3.3