Midterm Practice Exam

The daily high temperatures for one week in a mountain town were 18, 21, 19, 24, 22, 20, and 25 °C, which add to 149 °C. What is the mean daily high, in °C, rounded to four decimals? Enter the number only.

Type a short answer.

A clinic records the wait times of a sample of 75 patients, and a spreadsheet's STDEV.S returns 6.4 minutes. A coworker suggests reporting the variance instead. What are the units of each number, and which one belongs in a summary for patients?

Select one.

• Both are in minutes; either one can be reported
• The SD is in square minutes and the variance in minutes; report the variance
• The SD is in minutes and the variance in square minutes; report the SD
• Both have no units; report the variance because it is larger

A whole number is picked at random from 1 through 30. The event "the number is even" has 15 of the 30 outcomes, the event "the number is a multiple of 5" has 6 of the 30 outcomes, and 10, 20, and 30 belong to both. What is P(even or multiple of 5)?

Select one.

• 18 ⁄ 30
• 21 ⁄ 30
• 3 ⁄ 30
• 15 ⁄ 30

At a walk-in clinic, every one of the 40 patients who tested positive for strep throat had a sore throat, and 160 patients in all had a sore throat. True or false: P(sore throat | positive strep test) is equal to P(positive strep test | sore throat).

True or false.

• True
• False

A fair coin is flipped and a fair six-sided die is rolled, and neither affects the other. P(heads) = 1 ⁄ 2 and P(the die shows six) = 1 ⁄ 6. What is the probability of heads and a six together?

Select one.

• 2 ⁄ 3
• 1 ⁄ 12
• 1 ⁄ 6
• 1 ⁄ 2

A common year has exactly twelve months, and all twelve month lengths are listed, so they form a whole population with N = 12. Their average length is 30.4167 days. Which label fits this 30.4167?

Select one.

• A statistic, because it is rounded to four decimal places
• A statistic, because twelve values make a small sample
• Neither, because a month is a category, not a number
• A parameter, because it describes every month in the population

A health researcher wants two graphs from a study of adults: one showing the distribution of resting heart rate by itself, and one showing how resting heart rate relates to hours of weekly exercise. Which pair of graphs fits?

Select one.

• A pie chart of heart rate, then a bar chart of both variables
• A scatterplot of heart rate alone, then a histogram of both variables
• A histogram of heart rate, then a scatterplot of heart rate and exercise
• A bar chart of heart rate, then a two-way table of both variables

On a youth soccer roster of 11 players, Q1 = 14 years and Q3 = 16 years, so the IQR is 2 years and the fences of the 1.5 × IQR rule are 11 and 19 years. The youngest player is a 10-year-old who was moved up an age group, and the oldest player is 17. Select every true statement.

Select every option that applies.

• The 10-year-old's age is flagged as a potential outlier
• The 10-year-old's age is a genuine value, so it stays in the data
• The 10-year-old must be removed because the age is flagged
• No player's age lies above the upper fence of 19 years
• Every player older than 16 is flagged because 16 is Q3

A card is drawn at random from a stack numbered 1 through 20. Let B be the event "the card's number is at least 15". Which event is the complement of B?

Select one.

• The number is 15 or less
• The number is exactly 14
• The number is 20
• The number is 14 or less

For 60 used cars of one model, a scatterplot of age in years (across) and asking price (up) shows points falling from upper left to lower right in a tight band along a straight line, and the correlation is r = −0.91. Which description fits?

Select one.

• Weak, negative, and curved
• Strong, positive, and linear
• Strong, negative, and linear
• Moderate, negative, and clustered

A gym asks its members which of its six group classes they have attended this year, and members may name as many classes as they like. The class percentages add up to far more than the whole membership. Which graph shows these results honestly?

Select one.

• A bar chart, because one member can fall in several categories
• A pie chart, because the results are given as percentages
• A histogram, because the classes are counted in bins
• A dot plot, because it shows each member's answer

The twelve month lengths of a common year are every month there is, and their mean is 30.4167 days. Which label and symbol fit this mean?

Select one.

• A statistic, written x̄, because it was rounded from data
• A parameter, written x̄, because the months are a whole population
• A parameter, written μ, because the twelve months are a whole population
• A statistic, written μ, because twelve values are a small sample

Each ticket in a fundraiser raffle pays $0, $5, or $50, and the expected payout is E(W) = $1.40 per ticket. True or false: this means a ticket holder should expect to receive about $1.40 from one ticket.

True or false.

• True
• False

A histogram of the sale prices of 200 homes sold in a town last year has its main pile in the lower price bins and a long, thinning tail of expensive homes. The middle price is $310,000, and the average price is $356,500. Which conclusion fits this evidence?

Select one.

• Left-skewed, because the average is the larger of the two prices
• Right-skewed, because the average sits above the middle price
• Symmetric, because the two prices are within $50,000 of each other
• Bimodal, because the average and the middle price are different

A bar chart compares two phone plans: Plan A costs $46 a month and Plan B costs $52. The vertical axis starts at $40, so Plan A's bar is drawn 6 units tall and Plan B's bar 12 units tall. Which statement is accurate?

Select one.

• Plan B really costs about twice as much as Plan A
• The chart is accurate, because each bar's height is measured correctly from the $40 baseline
• Plan A costs about 88.5% as much as Plan B, so the chart exaggerates a $6 gap
• The chart misleads only because its bars do not touch

Suppose each of 40 patients at a clinic independently has a 0.1 chance of a mild side effect, and X counts the patients who have one. Using this course's large-counts rule of thumb, may a normal curve stand in for the distribution of X?

Select one.

• Yes, because n = 40 patients is at least 10
• No, because np = 4 is below 10
• Yes, because the mean 4 is smaller than n
• No, because p = 0.1 is below 0.5

Across many fires, the number of firefighters sent and the dollar damage done tend to rise together. True or false: the size of the fire is a lurking variable that could produce this association without the firefighters causing the damage.

True or false.

• True
• False

A coffee cart's daily number of drinks sold, D, has mean 240 drinks and standard deviation 35 drinks. Each drink earns $1.50 in profit, so the daily profit is R = 1.5 × D dollars. Which pair gives E(R) and SD(R)?

Select one.

• E(R) = $360.00 and SD(R) = $35.00
• E(R) = $360.00 and SD(R) = $52.50
• E(R) = $241.50 and SD(R) = $36.50
• E(R) = $160.00 and SD(R) ≈ $23.33

A shuttle arrives at a random moment in a 20-minute window, so its arrival time T, in minutes, has a flat density curve of height 1 ⁄ 20 from 0 to 20. What is P(5 ≤ T ≤ 12)?

Select one.

• 1 ⁄ 20
• 7
• 0.35
• 0

A simple model for a ball tossed straight up, with gravity rounded to 10 meters per second per second, gives its height above the ground at 0, 1, 2, 3, and 4 seconds as 0, 15, 20, 15, and 0 meters. The five points form a perfect upside-down U, and the correlation between time and height is 0. What does that correlation of 0 tell you?

Select one.

• Time and height have no relationship at all
• The heights must be wrong, since a perfect pattern always has r = 1
• The relationship is weak, so time only slightly affects height
• There is no straight-line trend, even though height depends completely on time

A prize wheel pays 1, 3, 5, or 7 tokens, each with probability 1 ⁄ 4, so the mean payout is 4 tokens. The four squared deviations from the mean are 9, 1, 1, and 9, which add to 20. What is the variance Var(X)?

Select one.

• 20 ⁄ 4 = 5 square tokens
• 20 ⁄ 3 ≈ 6.6667 square tokens
• 20 square tokens
• √5 ≈ 2.24 square tokens

A stem plot of the ages of 14 volunteers uses the tens digit as the stem: stem 1 holds the leaves 8 9; stem 2 holds the leaves 0 2 2 2 5 7; stem 3 holds the leaves 1 4 4; stem 4 holds the leaves 0 6 9. How many volunteers are exactly 22 years old?

Select one.

• 3
• 6
• 22
• 14

A campus survey counted students by class year and by where they usually eat lunch, as shown in this two-way table.

How many students in all usually eat lunch from the food truck? Enter a whole number.

Type a short answer.

In an observational study of 500 office workers, the people who drank the most coffee also worked the most hours each week. Therefore, this study shows that drinking coffee causes people to work longer hours.

True or false.

• True
• False

A carnival game awards X points. The values 0, 1, 2, and 5 happen in 8, 6, 4, and 2 of the 20 equally likely outcomes, and the products of each value and its number of outcomes add to 24. What is the expected value E(X)? Enter a number.

Type a short answer.