Q: A histogram shows the number of days 105 patients were depressed prior to treatment. If 8 patients had 0–60 days, 12 had 61–120 days, 28 had 121–180 days, 25 had 181–240 days, and the rest had more, what percentage of patients had fewer than 180 days of depression? (Round your answer to two decimal places.)

$$\frac{8+12+28}{105} \times 100 = 45.71\%$$

Q: A boxplot shows the ages of Oscar-winning actors: min = 31, Q1 = 37.5, median = 42.5, Q3 = 49.5, max = 76. Is the maximum value (76) an outlier? Use the 1.5*IQR rule.

No, because $$76 \u003c Q3 + 1.5 \times (Q3 - Q1)$$

Q: Given the regression equation $$y = 5006 - 491x$$ for predicting the NASDAQ Index (y) from bond rate (x), what is the predicted NASDAQ Index for a bond rate of $$7.5\%$$?

$$y = 5006 - 491 \times 7.5 = 5006 - 3682.5 = 1323.5$$

Q: A regression model for city mortality rate (y) and education level (x) is $$y = -49.92x + 1493.3. $$What is the predicted mortality rate for a city with an education level of $$10.25$$ years?

$$y = -49.92 \times 10.25 + 1493.3 = -511.68 + 1493.3 = 981.62$$

Q: Given the probability distribution for $$Y$$, the number of people in an apartment: $$P(Y=0)=0.05$$, $$P(Y=1)=0.05$$, $$P(Y=2)=0.10$$, $$P(Y=3)=0.75$$, $$P(Y=4)=0.05. $$What is the mean of $$Y$$?

$$\mu = 0 \times 0.05 + 1 \times 0.05 + 2 \times 0.10 + 3 \times 0.75 + 4 \times 0.05 = 2.7$$

Question 1

A Gallup study collected the following information about recent college graduates: annual income, employment status (employed or unemployed), zip code, undergraduate GPA, and whether the graduate was a member of a sorority/fraternity. Which of the following is a quantitative variable?

Accepted Answer

Undergraduate GPA

Question 2

Which of the following is a qualitative variable from the Gallup study described above?

Accepted Answer

Employment status

Question 3

A histogram of calcium concentration (ppm) in drinking water is right-skewed. The summary statistics are: $$	ext{Median} = 24.6$$, $$	ext{Mean} = 47.8$$, $$	ext{Q}_1 = 6.5$$, $$	ext{Q}_3 = 205.2. $$Which of the following statements is most likely true?

Accepted Answer

The mean calcium (ppm) is greater than the median calcium (ppm) because the distribution is right-skewed.

Question 4

A histogram shows the number of days 105 patients were depressed prior to treatment. If 8 patients had 0–60 days, 12 had 61–120 days, 28 had 121–180 days, 25 had 181–240 days, and the rest had more, what percentage of patients had fewer than 180 days of depression? (Round your answer to two decimal places.)

Accepted Answer

$$\frac{8+12+28}{105} 	imes 100 = 45.71\%$$

Question 5

A study surveyed people on how many phone calls they made daily. The frequency table is: 1–4 calls: 16, 5–8: 11, 9–12: 5, 13–16: 3, 17–20: 2. How many people made more than 8 phone calls daily?

Accepted Answer

21

Question 6

Given the same phone call frequency table, within which interval will the median fall?

Accepted Answer

5–8

Question 7

A boxplot shows the ages of Oscar-winning actors: min = 31, Q1 = 37.5, median = 42.5, Q3 = 49.5, max = 76. Is the maximum value (76) an outlier? Use the 1.5*IQR rule.

Accepted Answer

No, because $$76 \u003c Q3 + 1.5 	imes (Q3 - Q1)$$

Question 8

A calculus exam has $$Q3 = 79$$ and an upper fence of $$94. $$Would a score of $$55 be $$considered an outlier using the 1.5*IQR criterion?

Accepted Answer

No, because $$55 is $$above the lower fence

Question 9

Given the regression equation $$y = 5006 - 491x$$ for predicting the NASDAQ Index (y) from bond rate (x), what is the predicted NASDAQ Index for a bond rate of $$7.5\%$$?

Accepted Answer

$$y = 5006 - 491 	imes 7.5 = 5006 - 3682.5 = 1323.5$$

Question 10

A regression model for city mortality rate (y) and education level (x) is $$y = -49.92x + 1493.3. $$What is the predicted mortality rate for a city with an education level of $$10.25$$ years?

Accepted Answer

$$y = -49.92 	imes 10.25 + 1493.3 = -511.68 + 1493.3 = 981.62$$

Question 11

Which of the following statements about the linear correlation coefficient $$r is $$FALSE?

Accepted Answer

The linear correlation coefficient $$r is $$expressed in units based on the scale of the explanatory and response variables.

Question 12

What is the probability of rolling a 5 on one roll of a fair six-sided die?

Accepted Answer

$$\frac{1}{6}$$

Question 13

What is the probability of rolling a 5 on the first roll and a 6 on the second roll of a fair six-sided die?

Accepted Answer

$$\frac{1}{36}$$

Question 14

A carnival game involves a spinner and a roll of a fair six-sided die. The spinner has 3 equally likely spaces numbered 1, 2, and 3. Your score is the product of the spinner number and the die number. You win a prize if your score is 6 or 12. What is the probability of winning a prize in this game?

Accepted Answer

$$\frac{5}{18}$$

Question 15

Given the probability distribution for $$Y$$, the number of people in an apartment: $$P(Y=0)=0.05$$, $$P(Y=1)=0.05$$, $$P(Y=2)=0.10$$, $$P(Y=3)=0.75$$, $$P(Y=4)=0.05. $$What is the mean of $$Y$$?

Accepted Answer

$$\mu = 0 	imes 0.05 + 1 	imes 0.05 + 2 	imes 0.10 + 3 	imes 0.75 + 4 	imes 0.05 = 2.7$$

Question 16

A histogram of tip amounts at a restaurant shows frequencies: $$0-2: 39$$, $$2-4: 64$$, $$4-6: 32$$, $$6-8: 11$$, $$8-10: 8$$, $$10-12: 2$$, $$12-14: 1$$, $$14-16: 1. $$What is the sample size for this data set?

Accepted Answer

$$39+64+32+11+8+2+1+1=158$$

Question 17

In a histogram of depression days for 105 patients, which of the following is a possible value of the median number of days depressed?

Accepted Answer

170

Question 18

Which of the following is most likely to be true for a right-skewed distribution of depression days?

Accepted Answer

The mean will be larger than the median

Statistics Study Guide: Variables, Data Displays, Probability, and Regression

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