mid

A group of students played a game in which they earned points for answering questions correctly. The following dotplot shows the total number of points earned by each student.
Which of the following is the best description of the distribution of points earned?

Bimodal with gap

The table shows the responses from 103 people when asked if they support a proposal to expand the public library.
One person from those who responded will be selected at random. Which of the following is closest to the probability that the person will be someone who responded no, given that the person selected is age 55 or older?

0.818 (36/44)

Data were collected on the fiber diameter and the fleece weight of the wool taken from a sample of 20 sheep. The data are shown in the following graphs. Graph 1 is a scatterplot of fleece weight versus fiber diameter with the respective least- squares regression line shown. Graph 2 is the associated plot of the residuals versus the predicted values.
One point is circled on graph 1. Five point labeled A, B, C, D, and E are identified on graph 2. Which point on graph 2 represents the residual for the circled point on graph 1?

point c

The distributions of four variables are shown in the following histograms. Which of the following shapes is NOT represented by one of the four distributions?

uniform

A random sample of 1,092 people were asked whether color was a consideration in buying a new car. They were also asked to identify one additional feature that was important. The responses are shown in the table.
Which of the following is closest to the proportion of people who responded no to color consideration and who identified safety as the additional feature that was important?

0.18 (192/1092 = 0.175)

Scientists estimate that the distribution of the life span of the Galapagos Islands giant tortoise is approximately normal with mean 100 years and standard deviation 15 years. based on the estimate, which of the following is closest to the age of the Galapagos Islands giant tortoise at the 90th percentile of the distribution ?

120 years ( inverse norm on calc, area = 0.9, mean = 100, SD= 15)

A car rental agency has two locations in a city. The boxplots below summarize the miles driven for one day of single- day car rentals at each location.
Based on the boxplots, which statement provides the best comparison of the two locations?

Compared with location A, the miles driven for location B display more variability, and the median is greater.

For the purpose of determining the value of its end of year inventory, a clothing store creates a list at the end of the year of every item in stock along with each items wholesale price.
Which of the following is the best description of the end of year activity?

A census, because the wholesale prices of all items are listed. (Census= everything... a sample would leave items out and not be accurate)

A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn with mean weight 1.26 pounds. The standard deviation of the weights of corn form the farm in Ohio s 0.01 pound greater than that from the farm in Iowa. A randomly selected ear of corn from the farm in Iowa weighed 1.39 pounds, which has a standardized score of 1.645 for the distribution of weights for the Iowa corn. If an ear of corn from the farm in Ohio weighs 1.39 pounds, how many standard deviations from the mean is the weight with respect to the Ohio distribution?

1.46 standard deviations above the mean ( z score= x- mean/ SD) 1.645= 1.39- 1.26/ SD of Ohio- 0.01
SD of Ohio - 0.01 = 0.13/ 1.645
SD of Ohio = 0.089

The distribution of number of hours worked by volunteers last year at a large hospital is approximately normal with mean 80 and SD 7. Volunteers in the top 20 percent of hours worked will receive a certificate of merit. IF a volunteer from last year is selected at random, which of the following is closest to the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer has worked is less than 90?

0.134
norm cdf
0.127/ 0.923 = 0.138

Resting hear rates in beats per minute were recorded for two sample of people. One sample was from people in the age group of 20 to 30 years and the other sample was from people in the age group of 40 to 50 years. The five number summaries are shown in the table.
The values 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age group 20 years to 30 years because they are either 1.5 times the IQR greater than the upper quartile of 1.5 times the IQR less than the lower quartile.
Using the same method for identifying outliers, which of the following values are identified as outliers for the age group 40 years to 50 years?

Only 60 is identified as an outlier.
(1.5 x 6 = 9)
(Q3-Q1= IQR)
(76-70= 6)
(Q3+9= 85)
(Q1-9= 61)

As a part of a demographic study, a college administrator needed to survey a sample of students from the college. From each major offered at the college, the administrator randomly selected 5 percent of the students with that major to participate in the survey.
Which of the following is the best description of the type of sample selected by the administrator?

Stratified random sample (ex: male/ female, age, etc)

The graph shows the population distribution of random variable X with mean 85 and SD 18.
Which of the following graphs is a sampling distribution of the sample mean X for samples of size 40 taken from the population?

B

The director of a community recreation center conducted a 6 week study to examine the effects of 4 types of exercise- strength training, flexibility, aerobics, and jogging - on maximal oxygen consumption. From the 40 members who participated, the director randomly assigned 10 members to each exercise type. Maximal oxygen consumption was measured for each member at the beginning of the study and again at the end of the six weeks. The director examined the change in maximal oxygen consumption for each member. Which of the following statements is correct description of a feature of the study?

The treatments in the study are strength training, flexibility training. aerobics, and jogging.

Sean and Evan are college roommates who have part time jobs are servers in restaurants. The distribution of Sean's weekly income is approximately normal with mean 225$ and SD of 25$. The distribution of Evan's weekly income is approximately normal with mean 240 $ and SD of 15 $. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?

0.303
(25^2 + 15^2 = 850)
(sqrt of 850 =29.158 which is about 0.303)

According to data from the US Elections Project only 36 % of eligible voters voted in the 2014 elections. For random samples of size 40, which of the following best describes the sampling distribution of p hat, the sample proportion of people who voted in the 2014 elections?

The sampling distribution is approximately normal, with mean 0.36 and SD 0.076.
(SD= sqrt p(1-p)/ n)
sqrt 0.36 (1- 0.36)/ 40 = .076

To investigate whether the consumption of beetroot juice enhances performance, a researcher selected a random sample of 50 student athletes from all the student athletes at a college. The athletes in the sample were randomly assigned to one of two groups. In one group, 25 athletes, were given a daily dose of beetroot juice, and in the other group, the remaining athletes were given a daily does of a placebo. At the end of 6 weeks of exercise training, the researcher compared the performances, of the two groups. Based on the design of the investigation, which of the following is the largest population to which the results can be generalized?

All student athletes at the college

Colleges researchers wanted to know under what conditions people are more likely to complete and return a survey. As part of a study, the researchers prepared three sets of identical surveys and used three methods of delivering and returning the surveys. The methods are described as follows... The graph shows the percent of surveys returned and not returned for each delivery method.

The In Class delivery method had the greatest rate of return, and the Dining Hall delivery method had the least rate of return.

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?

The proportion of the variation in height that is explained by a regression on age is 0.64

At a certain restaurant, the distribution of wait times between ordering a meal and receiving the meal has mean 11.4 minutes and standard deviation 2.6 minutes. The restaurant manager wants to find the probability that the mean wait time will be greater than 12.0 minutes for a random sample of 84 customers. Assuming the wait times among customers are independent, which of the following describes the sampling distribution of the sample mean wait time for random samples of size 84 ?

Approximately normal with mean 11.4 minutes and standard deviation 2.6/√84 minute. B

The histogram shows the distribution of heights, in inches, of 100 adult men. Based on the histogram, which of the following is closest to the interquartile range, in inches, of the distribution?

5

A city department of transportation studied traffic congestion on a certain highway. To encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2. The probability distribution of the number of people in passenger cars on the highway is shown in the table.
Based on the probability distribution, what is the mean number of people in passenger cars on the highway?

1.7

To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a randomized block design in which the subjects were blocked by age-group (under 40 years and 40 years or older). Which of the following must be true about the randomized block design of the experiment?

Treatments are randomly assigned to subjects within each block.

A die used in a certain board game has eight faces, of which 3 are red, 3 are yellow, and 2 are blue. Each face is equally likely to land faceup when the die is tossed. In the game, a player tosses the die until blue lands faceup, and the number of tosses before blue lands faceup is counted. For example, a player who tosses the sequence shown in the following table has tossed the die 3times before blue lands faceup.
What is the probability that a player will toss the die at least 2 times before blue lands faceup?

0.5625

High school students from track teams in the state participated in a training program to improve running times. Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds. After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30seconds. Let X represent the running time of a randomly selected student before training, and let Y represent the running time of the same student after training. Which of the following is true about the distribution of X−Y ?

The variables X and Y are not independent; therefore, the mean is 34 seconds and the standard deviation cannot be determined with the information given.

In northwest Pennsylvania, a zoologist recorded the ages, in months, of 55 bears and whether each bear was male or female. The data are shown in the back-to-back stemplot below.

The median age and the range of ages are both greater for female bears than for male bears.

Researchers working for a certain airline are investigating the weight of carry-on bags. The researchers will use the mean weight of a random sample of 800 carry-on bags to estimate the mean weight of all carry-on bags for the airline. Which of the following best describes the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300?

The bias will remain the same and the variance will decrease. C

A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately ¼ of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item?

1-(3/4)^4

A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer's batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem?

The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.

Nutritionists examined the sodium content of different brands of potato chips. Each brand was classified as either healthy or regular based on how the chips were marketed to the public. The sodium contents, in milligrams (mg) per serving, of the chips are summarized in the boxplots below. Based on the boxplots, compare the two classifications of the sodium content of the chips

The interquartile range (IQR) of the brands classified as healthy is greater than the IQR of the brands classified as regular.

The director of a technical school was curious about whether there is a relationship between students who complete one of the school's most popular Health Sciences certificate programs and whether their students go on to complete more advanced studies in the Health Sciences within two years of completing the certificate program. She randomly selected 100 students who completed the program. Data collected on these students are shown in the table below. Which of the following statements is true for these 100 students?

Being a person who did not complete the program but completed more advanced studies is less likely than being a person who completed the program and completed more advanced studies.

The figure above summarizes the heights, in centimeters, of approximately 400 pine seedlings six years after they were planted at a center of environmental study. Approximately half of the trees were fertilized yearly, and the remaining trees were never fertilized. Which of the following statements about the medians and interquartile ranges (IQRs) of the heights of the two groups of trees 6 years after being planted is true?

The median for the unfertilized trees is less than the median for the fertilized trees, and the IQR is greater for the unfertilized trees.

Grain moisture is a characteristic of grain that affects the price paid for the grain. A random sample of 28 loads of corn was evaluated for moisture as a percent of the total weight. A different random sample of 28 loads of soybeans was also evaluated for moisture. The data are displayed in the dotplots below.

the range

Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?

P(D or E) = 0.72

The histogram shown summarizes the responses of 100 people when asked,"What was the price of the last meal you purchased?"

Based on the histogram, which of the following could be the interquartile range of the prices?

$5

A sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies?

D) 16.5

The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer.
Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the expected cost per customer for the performance?

$29.40

For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season?

350 yards

A program that was intended to cure a person's fear of spiders was offered at a local zoo. Volunteers with a fear of spiders participated in the program, which included holding a spider for 15 minutes. Based on the description of the program, which of the following statements is true?

Because the participants were self-selected, a person's desire to be cured could be a confounding variable

At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables show the distribution responses?

(C)

Adults: 50, 20, 70
Children: 100, 40, 140

A scientist recorded the duration of the eruptions of the Old Faithful geyser in Yellowstone National Park that occurred during a one-month time period. The histogram below shows the distribution of the duration, in seconds, of the eruptions.

The distribution displays two clusters, with one cluster centered at about 125 seconds and the other centered at about 260 seconds, and has a range of at most 250 seconds.

There were 5317 previously owned homes sold in a western city in the year 2000. The distribution of the sale prices was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If we take many simple random samples of size 100 from this population and calculate the mean for each sample, which of the following describes the sample distribution of the sample mean?

Approximately normal with mean $206,274 and standard deviation $3,788.

Based on records kept at a gas station, the distribution of gallons of gas purchased by customers is skewed to the right with mean 10 gallons and standard deviation 4 gallons. A random sample of 64 customer receipts was selected, and the sample mean number of gallons was recorded. Suppose the process of selecting a random sample of 64 receipts and recording the sample mean number of gallons was repeated for a total of 100 samples. Which of the following is the best description of a dotplot created from the 100 sample means?

D) The dotplot is approximately normal with mean 10 gallons and standard deviation 0.5 gallon.

Based on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. Assume that in one practice Luke will attempt 5 shots of the arrow and that each shot is independent from the others. Let the random variable X represent the number of times he hits the inner ring of the target in 5 attempts. The probability distribution of X is given in the table.What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X ?

0.40951

A pharmaceutical company manufactures medicine to reduce pain caused by migraine headaches. The company is investigating whether a new medicine is more effective in reducing pain than the current medication. A random sample of 500 participants who experience migraines was selected, and the participants were randomly assigned to one of the two groups of equal size. The first group received the current medicine and the second group received the second medicine. When a participant got a migraine, they were instructed to take the medicine and, 15 minutes after taking the medicine, to rate the pain relief on a scale from 1 to 10, 1=no relief, 10=complete relief. At the end of the 6 months, the average pain relief for each participant was calculated. Which of the following is a description of the study.

A) An experiment using a completely randomized design

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

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?

n = 100 and p close to 1/2

In a standard golf tournament, golfers play 18 holes of golf on each of 4 consecutive days. For each hole, golfers keep track of the number of times they hit the ball (strokes) before the ball goes into the cup. A golfer's score for the tournament is the total number of strokes needed to complete the tournament. The boxplots below summarize the scores for golfers who competed in tournament 1 and golfers who competed in tournament 2. Based on the boxplots, which of the following statements must be true?

In both tournaments, at least half the golfers completed the tournament with a score less than 288.