1

A researcher claims that the average height of students at a school is 160 cm. A sample of 25 students is taken, and their average height is found to be 158 cm, with a standard deviation of 5 cm. We need to test the researcher’s claim using a significance level of 0.05.

A) Failure to reject the null hypothesis; insufficient evidence to reject the claim.

B) Reject the null hypothesis, the average height is 158 cm.

C) Reject the null hypothesis, the average height is not 160 cm.

D) Failing to reject the null hypothesis, the average height is exactly 158 cm.

2

A survey of 200 people found that 45 prefer a new brand of coffee. Construct a 95% confidence interval for the proportion of people who favor this new brand.

A) Between (0.67, 0.83)

B) Between (0.71, 0.23)

C) Between (0.51, 0.41)

D) Between (0.167, 0.283)

3

A researcher asserts that the average height of a specific plant species is 150 cm. A sample of 20 plants shows an average height of 145 cm, with a standard deviation of 10 cm. We will test the researcher’s claim at a significance level of 0.05.

A) Fail to reject the null hypothesis; the average height is 150 cm.

B) Reject the null hypothesis, evidence suggests the mean is not 150 cm.

C) Fail to reject the null hypothesis; there is insufficient evidence to conclude that the average height differs from 150 cm.

D) Reject the null hypothesis; the average height is exactly 145 cm.

4

A survey of 50 students found that the average number of hours they study per week is 20 hours, with a standard deviation of 4 hours. Using this data, we can construct a 95% confidence interval for the average number of hours that all students study per week.

A) Between 18.89 and 22.36

B) Between 19.23 and 21.11

C) Between 18.89 and 21.11

D) Between 19.23 and 22.89

5

A set of test scores includes: 65, 70, 75, 80, 85, 90, 95, and 100. Calculate the mean and median of these scores.

A) Mean = 82.5, Median = 85

B) Mean = 80, Median = 80

C) Mean = 85, Median = 82.5

D) Mean = 82.5, Median = 82.5

6

A factory claims that a product’s average weight is 500 grams. A sample of 25 products has a mean weight of 485 grams and a standard deviation of 15 grams. Test the factory’s claim at the 0.01 significance level.

A) The average weight is 500 grams.

B) The sample does not provide enough evidence.

C) Evidence suggests the mean is not 500 g.

D) The average weight is exactly 485 grams.

7

In a survey of 200 people, 140 stated that they prefer the new product over the old one. Construct a 95% confidence interval for the proportion of people who favor the new product.

A) Between 63.7% and 76.4%

B) Between 63.65% and 77.23%

C) Between 64.65% and 76.35%

D) Between 68.36% and 78.56%

8

A die is rolled 60 times, and the outcomes are recorded as follows: 1: 8, 2: 10, 3: 12, 4: 6, 5: 14, and 6: 10. We will test whether the die is fair at the 0.05 significance level.

A) Evidence suggests the die is unfair.

B) There is insufficient evidence to conclude the die is biased.

C) The die favors lower numbers.

D) The die is perfectly fair.

9

A school claims that 70% of its students participate in extracurricular activities. A random sample of 150 students found that 90 of them participated. Test the school’s claim at a significance level of 0.05.

A) Insufficient evidence to reject 70%.

B) The proportion is exactly 70%.

C) Evidence suggests the proportion is not 70%.

D) The proportion is significantly greater than 70%.

10

A random sample of 50 individuals has a mean age of 30 years and a standard deviation of 5 years. Construct a 99% confidence interval for the population mean age.

A) Between 28.18 and 31.82

B) Between 28.18 and 32.56

C) Between 29.36 and 31.82

D) Between 26.53 and 33.89