Q: Given the following frequency distribution for the age of mothers at birth, estimate the mean age at which a mother gives birth. Use the midpoint for each class and the frequencies: 10–14.99 (10), 15–19.99 (400), 20–24.99 (1050), 25–29.99 (1200), 30–34.99 (500), 35–39.99 (100), 40–44.99 (100).

$$\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{(12.5 \times 10) + (17.5 \times 400) + (22.5 \times 1050) + (27.5 \times 1200) + (32.5 \times 500) + (37.5 \times 100) + (42.5 \times 100)}{3360} \approx 26.5$$

Question 1

Which of the following variables is best classified as quantitative continuous?

Accepted Answer

Your monthly cell phone bill (dollars)

Question 2

A researcher divides 100 arthritis patients into two groups. One group receives a placebo while the other receives an experimental drug. The patients' levels of arthritis pain are then compared after 6 months. In this scenario, which is the explanatory variable?

Accepted Answer

The group assignment (placebo or drug)

Question 3

Which of the following is an example of a nominal level of measurement?

Accepted Answer

Eye color

Question 4

A statistics class with 37 students has 20 students majoring in Nursing and 16 students majoring in Engineering. If 5 students are randomly selected from the Nursing majors, and 3 students are randomly selected at random from the Engineering majors to form a sample of 8, what type of sampling method is this?

Accepted Answer

Stratified sampling

Question 5

Given the following data set of typing speeds (in words per minute): 42, 47, 52, 55, 55, 57, 60, 62, 65, 67, 68, 70, 72, 73, 75, 78, 80, 85, 90, 95. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 78 - 55 = 23$$

Question 6

A pie chart shows that 51% of people support new tolls, 34% support no new roads, and 15% support increasing the gas tax to pay for new road construction. What is the frequency of people supporting new tolls in a sample of 200 people?

Accepted Answer

$$0.51 	imes 200 = 102$$

Question 7

The population mean and standard deviation of weights for 20–29 year old females are $$\mu = 155$$ and $$\sigma = 50. $$What is the $$z-$$score for a 20–29 year old female who weighs 160 pounds?

Accepted Answer

$$z = \frac{160 - 155}{50} = 0.10$$

Question 8

A histogram of HDL cholesterol levels for 40 patients shows a peak in the 47–56 range and a tail to the right. Which term best describes the shape of this distribution?

Accepted Answer

Skewed right

Question 9

Given the following frequency distribution for the age of mothers at birth, estimate the mean age at which a mother gives birth. Use the midpoint for each class and the frequencies: 10–14.99 (10), 15–19.99 (400), 20–24.99 (1050), 25–29.99 (1200), 30–34.99 (500), 35–39.99 (100), 40–44.99 (100).

Accepted Answer

$$\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{(12.5 	imes 10) + (17.5 	imes 400) + (22.5 	imes 1050) + (27.5 	imes 1200) + (32.5 	imes 500) + (37.5 	imes 100) + (42.5 	imes 100)}{3360} \approx 26.5$$

Question 10

A boxplot is constructed for a data set of home prices in Los Angeles: 14500, 13999, 12999, 10995, 9980, 8998, 7889, 7200, 5500. Which of the following statements is correct about the presence of outliers?

Accepted Answer

The value 14500 is a potential outlier because it is much higher than the rest of the data.

Question 11

Which of the following best describes the difference between an experiment and an observational study?

Accepted Answer

An experiment involves manipulating variables, while an observational study does not.

Question 12

A researcher wants to estimate the average height of students at a university. She randomly selects every 5th student entering the library. What type of sampling method is this?

Accepted Answer

Systematic sampling

Question 13

Given the following five-number summary for a data set: Minimum = 42, $$Q_1 = 55$, Median = 65, Q_3$ = 78$$, Maximum = 95. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 78 - 55 = 23$$

Question 14

A frequency distribution of egg weights (in grams) has a mean of 1.615, a standard deviation of 0.1654, and a range of 1.27. What is the variance of the egg weights?

Accepted Answer

$$s^2$$ = $$(0.1654)^2 = 0.0274$

Question 15

Which of the following is a correct interpretation of the first quartile ($$Q_1) in a $$data set?

Accepted Answer

$$Q_1 is $$the value below which 25% of the data fall.

Question 16

A time-series plot of Google's closing stock prices from 2004 to 2010 shows a general upward trend with a dip in 2008. What real-world event most likely explains the dip in 2008?

Accepted Answer

The global financial crisis

Question 17

If a data set is skewed right, which of the following is most likely true about the relationship between the mean and the median?

Accepted Answer

The mean is greater than the median.

Question 18

A sample of 10 basketball players has heights (in inches): 76, 71, 70, 73, 73, 69, 77, 72, 68, 74. What is the population mean height?

Accepted Answer

$$\mu = \frac{76 + 71 + 70 + 73 + 73 + 69 + 77 + 72 + 68 + 74}{10} = 72.3$$

Statistics Study Guide: Data Types, Sampling, Descriptive Statistics, and Data Visualization

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