Question 1

Given the data set: 10, 12, 22, 25, 32, 40, 42, 48, calculate the mean. Which of the following is correct?

Accepted Answer

$$22.45$$

Question 2

Which formula correctly represents the standard deviation for a population?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum (x - \mu)^2$}{N}}$$

Question 3

A normal distribution has a mean of $$48$$ and a standard deviation of $$6. $$What is the $$z-$$score for an observation of $$36$$?

Accepted Answer

$$z = -2$$

Question 4

If the $$z-$$score for a value $$x is$$ $$1$$, the mean is $$40$$, and the standard deviation is $$6$$, what is the value of $$x$$?

Accepted Answer

$$x = 46$$

Question 5

Which of the following best describes the Empirical Rule for a normal distribution?

Accepted Answer

Approximately $$68\% of $$data falls within $$1$$ standard deviation, $$95\%$$ within $$2$$, and $$99.7\%$$ within $$3$$ standard deviations of the mean.

Question 6

Given the regression equation $$y = 42.65 - 1.68x_1 - 0.52x_2$$, what is the predicted $$y$$ when $$x_1 = 10$ and x_2$ = 20$$?

Accepted Answer

Question 7

A sample of small SUVs has the following miles per gallon: $$28, 31, 35, 39, 39, 39, 40, 43, 44, 47. $$What is the median?

Accepted Answer

$$39.5$$

Question 8

Which of the following is the correct formula for the mean of a sample?

Accepted Answer

$$\bar{x} = \frac{\sum x}{n}$$

Question 9

If a data set has a mean of $$850$$ and a standard deviation of $$50$$, what is the $$z-$$score for a value of $$750$$?

Accepted Answer

$$z = -2$$

Question 10

Which of the following statements about outliers is correct?

Accepted Answer

An outlier is a value that is more than $$1.5$$ times the interquartile range above the third quartile or below the first quartile.

Question 11

If the standard deviation of a data set is $$6$$ and the mean is $$48$$, what value is $$2.5$$ standard deviations below the mean?

Accepted Answer

$$33$$

Question 12

Which of the following best explains why the regression coefficient for insulation thickness is negative in the regression equation for natural gas consumption?

Accepted Answer

Increasing insulation thickness reduces natural gas consumption, holding other variables constant.

Question 13

A normal distribution has a mean of $$850$$ and a standard deviation of $$50. $$What percentage of observations fall between $$800$$ and $$900$$?

Accepted Answer

Approximately $$68\%$$

Question 14

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Question 15

If a value is $$1.5$$ interquartile ranges above the third quartile, what is it considered?

Accepted Answer

An outlier

Statistics Review: Measures, Boxplots, Normal Distribution, and Regression

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