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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
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