Question 1

A researcher collects the following data on the number of hours students study per week: 8, 10, 12, 14, 16. What is the sample mean ($$\bar{x}) of $$these values?

Accepted Answer

$$\bar{x} = \frac{8 + 10 + 12 + 14 + 16}{5} = 12$$

Question 2

Which measure of spread is most appropriate for a dataset with a strong right skew and several outliers?

Accepted Answer

Interquartile range (IQR)

Question 3

Given a sample of exam scores: 70, 75, 80, 85, 90, what is the sample standard deviation ($$s$$)?

Accepted Answer

$$s = \sqrt{\frac{(70-80)^2$ + (75-80)^2$ + (80-80)^2$ + (85-80)^2$ + (90-80)^2$}{5-1}} = \sqrt{\frac{100 + 25 + 0 + 25 + 100}{4}} = \sqrt{62.5} \approx 7.91$$

Question 4

A distribution is symmetric and bell-shaped. Which measures of center and spread should you use to describe it?

Accepted Answer

Mean and standard deviation

Question 5

The heights of adult males are normally distributed with mean $$\mu = 70$$ inches and standard deviation $$\sigma = 3$$ inches. What is the Z-score for a man who is 76 inches tall?

Accepted Answer

$$Z = \frac{76 - 70}{3} = 2$$

Question 6

A student scores 85 on a test where the mean is 80 and the standard deviation is 5. Interpret the student's Z-score.

Accepted Answer

The student's score is 1 standard deviation above the mean.

Question 7

In a normal distribution, what percentage of observations fall within two standard deviations of the mean according to the 68-95-99.7 rule?

Accepted Answer

95%

Question 8

A sample of five values has a mean of 10 and a standard deviation of 2. Which interpretation is correct?

Accepted Answer

On average, the observations fall 2 units away from the mean of 10.

Question 9

A researcher wants to reduce variation in an experiment by grouping similar subjects together before assigning treatments. What design should they use?

Accepted Answer

Block design

Question 10

If the area to the left of a Z-score is 0.975, what is the corresponding Z-score?

Accepted Answer

$$Z \approx 1.96$$

Question 11

A dataset has the following five-number summary: Min = 2, $$Q_1 = 4$$, Median = 6, $$Q_3 = 8$$, Max = 10. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 8 - 4 = 4$$

Question 12

A normal distribution has mean $$\mu = 50$$ and standard deviation $$\sigma = 10. $$What value marks the lowest 10% of the distribution?

Accepted Answer

$$x = \mu + Z \cdot \sigma = 50 + (-1.28) \cdot 10 = 37.2$$

Question 13

Which statement best describes the area under a density curve?

Accepted Answer

The area under a density curve is exactly 1, representing the total probability.

Question 14

A sample has values: 2, 4, 6, 8, 100. Which measure of center is most affected by the outlier?

Accepted Answer

Mean

Question 15

If a Z-score is negative, what does this indicate about the observation?

Accepted Answer

The observation is below the mean.

Question 16

A student uses a TI-84 calculator to find the probability that a value is between 60 and 80 in a normal distribution with mean 70 and standard deviation 5. Which command should they use?

Accepted Answer

normalcdf(60, 80, 70, 5)

Question 17

Which of the following best explains why block design is used in experiments?

Accepted Answer

To reduce variation by grouping similar subjects so the effect of the treatment can be seen more clearly.

Question 18

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What percent of values are expected to fall between 85 and 115?

Accepted Answer

68%

Question 19

Which formula is used to calculate the Z-score for an observation $$x in a $$normal distribution?

Accepted Answer

$$Z = \frac{x - \mu}{\sigma}$$

Statistics Exam Study Guide: Chapters 1, 2, 3, and 9 (Formula Sheet & Key Concepts)

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