Unit 1
Which of these variables are Quantative?
Hair color
speed of a car
shapes
Household income
Population
Speed of a car, household income, and population
A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?
Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.
An experiment was conducted to assess the effect of baking temperature on the density of bread. A large batch of white bread dough and a large batch of whole wheat bread dough were prepared. Each of the batches was formed into 18 loaves, resulting in a total of 36 loaves. Each of the white bread loaves was randomly assigned to one of three baking temperatures (low, medium, and high), so that 6 loaves were baked at the low temperature, 6 were baked at the medium temperature, and 6 were baked at the high temperature. A similar process of random assignment was carried out for the whole wheat bread loaves.
Which of the following are the treatments in the experiment?
a) The baking temperatures (low, medium, high)
b) The 36 loaves of bread
c) The type of bread (white, whole wheat)
a) The baking temperatures (low, medium, high)
A certain computer chip company has a machine that makes a large number of computer chips. Of the computer chips produced on this machine, 3% are defective. Miriam, the quality control inspector, will randomly select computer chips from the machine to inspect. What is the probability that the first defective computer chip Miriam finds is the sixth computer chip she inspects from the machine?
(0.97)⁵ (.03)
Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p̂?
a) n = 100 and p close to 0
b) n = 1,000 and p close to 1/2
c) n = 100 and p close to 1/2
c) n = 100 and p close to 1/2
A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?
a) There are more selling prices that are less than the mean than selling prices that are greater than the mean.
b) The value of maximum minus third quartile is less than the value of first quartile minus minimum.
c) The median is the average of the first quartile and the third quartile.
b) The value of maximum minus third quartile is less than the value of first quartile minus minimum.
Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale?
1
In a certain school, students can choose whether to eat in the school’s cafeteria. A reporter working for the school’s newspaper polled students on their reactions to changes in the menu at the cafeteria. For each student leaving the cafeteria in one 30-minute time period, the reporter used a coin to determine whether to stop the student and ask how he or she felt about the new menu. In the reporter’s article, it was stated that a random sample of the students showed that 89 percent of the school’s student population was happy with the new menu. Why might this high percentage be true?
Because students self-selected whether to eat in the cafeteria, the sampling method might be biased, and the sample might not be representative of all students in the school.
Ninety percent of the people who have a particular disease will have a positive result on a given diagnostic test. Ninety percent of the people who do not have the disease will have a negative result on this test. If 5 percent of a certain population has the disease, what percent of that population would test positive for the disease?
14%
The height requirement for a certain ride at an amusement park is 48 inches or taller. The distribution of height of six-year-old children is approximately normal with mean 45.2 inches and standard deviation 1.75 inches. Which of the following is closest to the probability that a randomly selected six-year-old child will not meet the height requirement for the ride?
a) 0.9452
b) 0.9599
C) 0.9974
a) 0.9452
Which of the following are discrete variables?
a) Height of players in the NBA, feet and inches
b) The battery life (time) of new cellphone models
c) The cost of a dinner for two at various restaurants
a) Height of players in the NBA, feet and inches
c) The cost of a dinner for two at various restaurants
Jacques, an artisan cheese maker, collects data on every step of the cheese-making process for each batch he makes. Jacques noticed that the daily high temperature in his shop on the day he made a batch of cheese was related to the pH of the cheese the next morning. He computed the correlation between the daily high temperature and the pH of the cheese to be −0.64. What information does the correlation provide about the relationship between the daily high temperature and the pH of the cheese?
The morning pH of the cheese tends to be higher when the daily high temperature in the shop is cooler, compared to when the daily high temperature is warmer.
A medical researcher conducted a study to investigate the effectiveness of two drugs, L and M, designed to reduce the number of seizures that people with epilepsy might have. Each person in a group of 120 adult volunteers who had epilepsy was randomly assigned to one of two groups. Those assigned to one group took drug L for one year, and those assigned to the other group took drug M for one year. Each participant recorded the number of seizures that occurred during the year.
To which group is it most reasonable to generalize the results of this study?
All adults with epilepsy who are similar to those who volunteered for the study
The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible items are chosen at random, one at a time, until one is found who purchased the extended warranty. Let the random variable X represent the number of customers it takes to find one who purchased the extended warranty. Assume customers’ decisions on whether to purchase the extended warranty are independent. Which of the following is closest to the probability that X>3; that is, the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty?
a) 0.493
b) 0.507
c) 0.624
a) 0.493
For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?
a) A random sample of 75 taken from a population distribution that is skewed to the left
b) A random sample of 10 was taken from a population distribution that is skewed to the right
c) A random sample of 8 taken from a normally distributed population
b) A random sample of 10 was taken from a population distribution that is skewed to the right
Suppose a new regulation requires businesses to pay all employees a minimum wage of $15.00 per hour. A small coffee shop currently has 9 employees—5 employees whose wages are less than $15.00 per hour and 4 employees whose wages are more than $15.00 per hour. To meet the new regulation, the coffee shop plans to increase the wages of the 5 employees whose wages are less than $15.00 per hour to $15.00 per hour. The other 4 employees will not receive a wage increase at this time.
Which of the following must be true about the median wage of the 9 employees after the wage increase occurs?
a) The median wage will not change.
b) The median wage will be $15.00 per hour.
c) The median wage will be greater than $15.00 per hour.
b) The median wage will be $15.00 per hour.
The relationship between carbon dioxide emissions and fuel efficiency of a certain car can be modeled by the least-squares regression equation ln(y^)=7−0.045x, where x represents the fuel efficiency, in miles per gallon, and y^ represents the predicted carbon dioxide emissions, in grams per mile.
Which of the following is closest to the predicted carbon dioxide emissions, in grams per mile, for a car of this type with a fuel efficiency of 20 miles per gallon?
a) 1.8
b) 6.1
c) 446
c) 446
A well-designed experiment should have which of the following characteristics?
I. Subjects assigned randomly to treatments
II. A control group or at least two treatment groups
III. Replication
I, II and III
A police officer is using a radar device to check motorists’ speeds. Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. Assuming that the police officer’s estimate is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?
0.8704
There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?
a) Approximately normal with mean $206,274 and standard deviation $3,788
b) Approximately normal with mean $206,274 and standard deviation $37,881
c) Strongly right-skewed with mean $206,274 and standard deviation $3,788
a) Approximately normal with mean $206,274 and standard deviation $3,788
The following is the number of ski accidents reports weekly, over 16 weeks, during one winter season at Super Slopes Resort.
11, 10, 5, 9, 15, 10, 6, 8, 2, 10, 7, 8, 16, 11, 12, 10
A concerned parent, Ms. Cooper disagrees with the ski resort's claims by saying "Yes, but half of these weeks there were 10 or more accidents. That's just not good enough"!
Which measure of central tendency was Ms. Cooper referencing?
The median
The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
a) The least-squares regression line will correctly predict height based on age 80% of the time.
b) The proportion of the variation in height that is explained by a regression on age is 0.64.
c) The least-squares regression line will correctly predict height based on age 64% of the time.
b) The proportion of the variation in height that is explained by a regression on age is 0.64.
A six-week training program was developed to help student athletes improve performance on a certain task. To study the effectiveness of the program, researchers randomly selected 50 student athletes. The students were tested before participating in the program. Then, half the athletes were randomly assigned to participate in the program and the other half were allowed to train on their own. At the end of the six weeks, all athletes were tested again. The researchers reported that the athletes who participated in the program increased their scores, on average, by 200 points, whereas those who did not participate raised their scores, on average, by 80 points.
After reading the results of the study, Jasmine, a student athlete, decided to enroll in the program. At the end of six weeks, her score had increased by 80 points. Which of the following is an explanation for the difference between Jasmine’s score and the scores that the study reported for student athletes who participated in the program?
a) The sample sizes used in the study were too small for any conclusions about the training to be valid.
b) The increase of 200 points reported was an average; some athletes could have increased their scores by more than 200 points, and some by less than 200 points.
c) Jasmine probably did not follow the program correctly; if she had, she would have seen a 200-point increase in her score.
b) The increase of 200 points reported was an average; some athletes could have increased their scores by more than 200 points, and some by less than 200 points.
According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 40?
(50/40) (.31)⁴⁰ (.69)¹⁰
a) The bias will decrease and the variance will remain the same.
b) The bias will remain the same and the variance will decrease.
c) The bias will remain the same and the variance will increase.
The bias will remain the same and the variance will decrease.