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Each of 133 children in a sample was asked to choose a pencil. Three different colors were available: yellow, red, and blue. The number of 2-year olds and 3-year olds who selected each color is shown in the table above. In a test of independence of age and color, which of the following is used as the expected cell count for 2-year olds who select a yellow pencil?
(14+28)(14+32+19)/133
A medical center conducted a study to investigate cholesterol levels in people who have had heart attacks. A random sample of 16 people was obtained from the names of all patients of the medical center who had a heart attack in the previous year. Of the people in the sample, the mean cholesterol level was 264.70 milligrams per deciliter (mg/dL) with standard deviation 42.12 mg/dL. Assuming all conditions for inference were met, which of the following is a 90 percent confidence interval for the mean ch the medical center who had a heart attack in the previous year?
(246.24, 284.16)
For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?
0.335
The following table shows the probability distribution for the number of books a student typically buys at the annual book fair held at an elementary school. Let the random variable B represent the number of books a student buys at the next book fair. What is the expected value of B?
1.79
A large city newspaper periodically reports the mean cost of dinner for two people at restaurants in the city. The newspaper staff will collect data from a random sample of restaurants in the city and estimate the mean price using a 90 percent confidence interval. In past years, the standard deviation has always been very close to $35. Assuming that the population standard deviation is $35, which of the following is the minimum sample size needed to obtain a margin of error of no more than $5 ?
113
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?
16.5
A group of men and women were surveyed to investigate the association between gender and the number of friends the person has on a social media Web site. Results are shown in the table above. Which of the following procedures is the most appropriate for investigating whether an association exists between gender and the number of friends a person has on a social media Web site?
A chi-square test of independence
A fitness center offers a one-month program designed to reduce body fat through exercise. The table shows the body fat percentage before and after completing the program for 10 randomly selected participants. The director of the program wants to investigate whether knowing the body fat percentage before beginning the program can help to predict body fat percentage for someone who completes the program. Which of the following procedures is the most appropriate for such an investigation?
A linear regression t-test for slope
A manufacturer claims its Brand A battery lasts longer than its competitor's Brand B battery. Nine batteries of each brand are tested independently, and the hours of battery life are shown in the table above. Provided that the assumptions for inference are met, which of the following tests should be conducted to determine if Brand A batteries do, in fact, last longer than Brand B batteries?
A one-sided, two-sample t-test
For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?
A random sample of 10 taken from a population distribution that is skewed to the right
A department store manager wants to know if a greater proportion of customers on the store's mailing list would redeem a coupon for $5 off the price of an item than would redeem a coupon for 10 percent off the price of an item. The manager mails a $5 off coupon to a random sample of 500 customers and mails a 10 percent off coupon to an independent random sample of 500 customers. The number of coupons of each type that were redeemed was recorded. Assuming that the conditions for inference are met, what test procedure should be used to answer the manager's question?
A two-sample z-test for a difference between two proportions
A dog food company wishes to test a new high-protein formula for puppy food to determine whether it promotes faster weight gain than the existing formula for that puppy food. Puppies participating in an experiment will be weighed at weaning (when they begin to eat puppy food) and will be weighed at one-month intervals for one year. In designing this experiment, the investigators wish to reduce the variability due to natural differences in puppy growth rates. Which of the following strategies is most appropriate for accomplishing this?
Block on dog breed and randomly assign puppies to existing and new formula groups within each breed.
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.
An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree. predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?
The height increases, on average, by 0.48 meter each year.
The bar chart displays the relative frequency of responses of students, by grade level, when asked, "Do you volunteer in a community-service activity?" Which of the following statements is not supported by the bar chart?
The number of tenth-grade students who responded yes was greater than the number of ninth grade students who responded yes.
A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, x, and the weight in tens of pounds, y. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years given by 1.272+/-0.570. Assume that the conditions for inference for the slope of the regression equation are met. Which of the following is the correct interpretation of the interval?
We are 95 percent confident that the mean increase in the weight of a black bear for each one-year increase in the age of the bear is between 7.0 and 18.4 pounds.
A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation of the 95 percent confidence level?
We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.
The probability of obtaining a head when a certain coin is flipped is about 0.65. Which of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times?
0.37
A consumer group wanted to investigate the relationship between the number of items purchased at a single visit to the local grocery store and the total cost of the items purchased. The group obtained a random sample of 11 receipts from the store and recorded the total number of items and the total cost from each receipt. The computer output of an analysis of total cost versus number of items purchased is shown in the table. Assume all conditions for inference were met. Based on the results shown in the table, which of the following is a 95 percent confidence interval for the average change in total cost for each increase of 1 item purchased?
2.784±2.262(0.2265)
A data set of test scores is being transformed by applying the following rule to each of the raw scores. Transformed score = 3.5(raw score) + 6.2 Which of the following is NOT true?
The range of the transformed scores equals 3.5(the range of the raw scores) + 6.2
Past studies indicate that about 60 percent of the trees in a forested region are classified as softwood. A botanist studying the region suspects that the proportion might be greater than 0.60. The botanist obtained a random sample of trees from the region and conducted a test of H0: p=0.6 versus Ha:p>0.6. The p-value of the test was 0.015. Which of the following is a correct interpretation of the p-value?
If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist.
A researcher conducting a telephone survey is concerned about possible sources of bias. Of the following, which is the best example of nonresponse bias?
Many of the people selected to participate in the survey who do not respond might have opinions different from those who do respond.
A researcher collected data on the age, in years, and the growth of sea turtles. The graph above is a residual plot of the regression of growth versus age. Does the residual plot support the appropriateness of a linear model?
No, because the graph displays a U-shaped pattern.
A program exists to encourage more middle school students to major in math and science when they go to college. The organizers of the program want to estimate the proportion of students who, after completing the program, go on to major in math or science in college. The organizers will select a sample of students from a list of all students who completed the program. Which of the following sampling methods describes a stratified random sample?
Randomly select 25 names from the female students on the list and randomly select 25 names from the male students on the list.
City officials estimate that 46 percent of all city residents are in favor of building a new city park. A random sample of 150 city residents will be selected. Suppose that 51 percent of the sample are in favor of building a new city park. Which of the following is true about the sampling distribution of the sample proportion for samples of size 150 ?
The distribution is approximately normal, and the mean is 0.46.