STA 261 CYU 1-5

Randomly select numbers 0-9. Let numbers 0-2 correspond to LeBron James, 3-4 correspond to Cristiano Ronaldo, 5 correspond to Danica Patrick, 6-7 correspond to Serena Williams, and 8-9 correspond to Floyd Mayweather. Below is a list of random numbers. How many boxes of cereal must you buy to obtain all 5 pictures. Report your answer in number form (for example, 2) 09979949167218518653

15

Find the expected number of girls in a family of four children. Do not round your answer.

2.16

Use StatCrunch to compute the value of the first quartile, Q1, and report it.

25

Use StatCrunch to find the mean. Do not round your answer.

29.75

Report the median.

31

Find the predicted mileage for a car which weighs 2400 pounds. Round your answer to one decimal place.

38.9

Use StatCrunch to find the standard deviation. Round your answer to three decimal places.

8.379

Use StatCrunch to find the 75th percentile. Round your answer to one decimal place.

98.1

A recent national census found that the median household income in a certain country was $68,100 and the mean was $72,100. Based on only this information, what would you predict about the shape of the distribution? Why?

The fact that the mean is higher than the median indicates that there are extremely high incomes that are affecting the mean, but not the median, suggesting that the shape is skewed to the right.

The z-score for an observation of 3 is -1.53. What does this z-score imply?

The observation 3 is 1.53 standard deviations below the mean. It is not an outlier because it is less than 3 standard deviations from the mean.

Explain why it does not make sense to compute the mean of this probability distribution as (0+1+2)/3 = 1.0.

The probabilities of each possible value are not all the same.

Twenty-five different cars were tested, and their weights (in pounds) and mileage (miles per gallon) were measured. Identify the natural response variable and explanatory variable.

The response variable is mileage and the explanatory variable is weight.

Interpret the y-intercept.

The y-intercept is the predicted miles per gallon for a car that weighs 0 pounds.

Identify the "who" in the news article.

US airlines

A car that weighs 2400 pounds has a predicted mileage of 38.9 miles per gallon. If the car has an observed mileage of 36 miles per gallon, find the residual.

-2.9

Use StatCrunch to find the proportion of children have an index of at least 110.

0.0478

For a given pair of free throws, estimate the probability that the player misses the second free throw. The probability is ___________.

0.12

The correlation coefficient of the regression between time spent watching TV and college GPA is -0.352. Find the coefficient of determination. Report your answer to four decimal places.

0.1239

Use StatCrunch to find the probability that the family has two girls and two boys.

0.3702

The mean is _________ languages. (Do not round your answer.)

1.06

The carbon dioxide emissions of a group of nations had a mean of 8.2 and a standard deviation of 3.4. Find the z-score for the observation of 14.5

1.85

If P(A) = 0.37, what is the P(not A)?

0.63

What is the probability that the player made both free throws? The probability is ___________.

0.74

This situation applies to the next 6 questions: One pro basketball player was known for being a good shooter. In games during 1980-1982, when he missed his first free throw, 48 out of 55 times he made the second one, and when he made his first free throw, 251 out of 285 times he made the second one. A contingency table organizing the data is below. The probability is ___________.

0.84

Estimate the probability that the player made the second free throw, given that he made the first free throw. The probability is ___________. (Round to the nearest hundredth as needed.)

0.88

For a given pair of free throws, estimate the probability that the player made the first or the second free throw. The probability is ___________.

0.98

What is the component to be repeated?

Buying a box of cereal.

Are making the first freethrow and making the second freethrow independent events?

False

If two variables are correlated, then there is a causal relationship between them.

False

When performing a simulation by hand, one trial is sufficient.

False

Interpret the slope in terms of a 1000-pound increase in the vehicle weight.

For each 1000-pound increase in the vehicle, the predicted mileage will decrease by 4.636 miles per gallon, on average.

For the following pair of variables, Grade received and Effort, which more naturally is the response variable and which is the explanatory variable?

Grade received is the response variable because it is the outcome variable on which comparisons are made and Effort is the explanatory variable.

Identify the appropriate measure of spread to report and the correct reason.

IQR; whenever there are outliers, we report the IQR.

Your friend decides to flip a coin repeatedly to analyze whether the probability of a head on each flip is ½. He flips the coin 20 times and observes a head 12 times. He concludes that the probability of a head for this coin is 12/20 = 0.60. Your friend claims that the coin is not balanced, since the probability is not 0.50. What's wrong with your friend's claim?

In the short run, the proportion of a given outcome can fluctuate a lot. A long run of observations is needed to accurately calculate the probability of flipping heads.

Identify the "when" in the news article.

May 11, 2020

What is the response variable?

Number of boxes of cereal necessary to obtain all 5 athletes' pictures.

Which statement below best distinguishes description from inference?

Statistical description provides useful summaries of the data, while inference helps make predictions and decide whether observed patterns are meaningful.

Identify the appropriate measure of center to report and the correct reason.

Outliers are present, so we should report the median.

Which of the following plans will work to model the component?

Randomly select numbers 0-9. Let numbers 0-2 correspond to LeBron James, 3-4 correspond to Cristiano Ronaldo, 5 correspond to Danica Patrick, 6-7 correspond to Serena Williams, and 8-9 correspond to Floyd Mayweather.

A social scientist uses a survey to study how much time per day people spend watching TV. The variable given on the survey website measures this using the values 0, 1, 2, ..., 24. Explain how, in theory, TV watching is a continuous random variable. Choose the correct answer below.

Someone could watch exactly 1 hour of TV or 1.8643 hours of TV.

Identify the shape of the distribution of professor salaries.

Right skewed

Is size of home (measured in square feet) a categorical or quantitative variable? Why?

Size of home is a quantitative variable. Its values are numerical.

The standard deviation, the range, and the interquartile range (IQR) summarize the variability of the data. Why is the IQR sometimes preferred to the standard deviation?

The IQR is not affected by an outlier, while the standard deviation is affected by an outlier.

Identify the "where" in the news article.

The New York Times

A travel magazine recently presented data on the annual number of vacation days averaged by residents of eight different countries. They reported 40 days for Italy, 37 for France, 35 for Germany, 33 for Brazil, 29 for Britain, 26 for Canada, 24 for Japan, and 14 for the United States. Use StatCrunch to graph the data. Select the letter that matches the best description of the distribution below.

The distribution is left skewed with no outliers, it has a median of 31 and an IQR of 11.

How many components will you have to combine into a single trial?

The answer will vary for each trial; once we have all 5 pictures we have completed a trial

The correlation coefficient of the regression between time spent watching TV and college GPA is -0.352. Select the correct interpretation.

The correlation of -0.352 indicates that there is a negative relation between the two variables. The more one watches TV, the lower his or her college GPA tends to be.

The conditional proportion of females who binge drink is 0.42, compared with 0.58 who don't. Based on these proportions and your earlier work, does it seem that there is an association between binge drinking and gender?

Yes. Binge drinking appears to be more prevalent among males.

Identify the "what" in the news article. Select all that apply.

average number of customers per flight and amount lost per day

When two explanatory variables are associated with the response variable and each other they are called __________ variables.

confounded

Simulations are done when

it is not practical to perform an experiment

Which of the below are the four conditions necessary for a binomial distribution?

trials are independent fixed number of trials 2 outcomes probability is the same for each trial

Select the correct regression equation.

y-hat = 49.987 - 0.0046x