stats unit eight review (final)
The local ranger station tracked and tagged 2,844 adult female black bears in a national park. A random sample of 9 adult female black bears from those tagged had an average body weight of 203 pounds with standard deviation 25 pounds. Which of the following is a point estimate for the population mean weight of all female black bears that are tagged?
203
Ecologists wanted to estimate the mean biomass (amount of vegetation) of a certain forested region. The ecologists divided the region into plots measuring 1 square meter each, and they selected a random sample of 9 plots. The mean biomass of the 9 plots was 4.3 kilograms per square meter ( kg/m2 ) and the standard deviation was 1.5 kg/m2 . Assuming all conditions for inference are met, which of the following is a 95 percent confidence interval for the population mean biomass, in kg/m2 ?
4.3±2.306(31.5)
Consider a 90 percent confidence interval to estimate a population proportion that is constructed from a sample proportion of 66 percent. If the width of the interval is 10 percent, what is the margin of error?
5 percent
Engineers at a tire manufacturing company investigated the effect of a new rubber compound on the tire life of a certain brand of tires. From a sample of 16 tires, the engineers constructed a 99 percent confidence interval for the mean tire life, in miles, as 62,550±2,026.62,550±2,026. Suppose the company intends to claim a maximum tire life for advertising purposes. Based on the interval, of the following, which is the maximum plausible value for the mean tire life, in miles?
64,500
Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. If the reported percent has a margin of error of 2.7 percentage points, which of the following is closest to the level of confidence?
90.0%
To study learned behavior in mice, researchers used a sample of mice in a maze experiment. Each mouse had to find its way through a maze to reach food at the end. The mouse was timed on its first run through the maze and again on its tenth run through the maze. The difference in the times was recorded for each mouse. Which of the following is the most appropriate inference procedure for the researchers to use?
A matched-pairs t-interval for a mean difference
A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate. Which of the following is an appropriate method for the biologist to use for inference to the population?
A one-sample t-interval for a population mean
A team of ecologists will select a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. Which of the following is a correct inference procedure for the ecologists to use?
A one-sample t-interval for a population mean
Environmentalists want to estimate the percent of trees in a large forest that are infested with a certain beetle. The environmentalists will select a random sample of trees to inspect. Which of the following is the most appropriate method for creating such an estimate?
A one-sample z-interval for a population proportion
The manager of a magazine wants to estimate the percent of magazine subscribers who approve of a new cover format. To gather data, the manager will select a random sample of subscribers. Which of the following is the most appropriate interval for the manager to use for such an estimate?
A one-sample z-interval for a population proportion
The superintendent of a large school district wants to estimate the percent of district residents who support the building of a new middle school. To gather data, the superintendent will select a random sample of district residents. Which of the following is the most appropriate method for creating such an estimate?
A one-sample z-interval for a population proportion
An environmental agency frequently samples the water in a region to ensure that the levels of a certain contaminant do not exceed 30 parts per billion (ppb). From 12 randomly selected samples of the water, the agency constructed the 99 percent confidence interval (22.5, 28.7).
We are 99 percent confident that the mean level of the contaminant in all the water in the region is between 22.5 ppb and 28.7 ppb
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.
For a t-distribution with sample size 10, P(t>1.96)≈0.0408P(t>1.96)≈0.0408 and P(t≤−1.96)≈0.0408P(t≤−1.96)≈0.0408. Which of the following is a property of the t-distribution illustrated by the probabilities?
With sample size 10, the tails of the curve of the t-distribution have more area than the tails of the curve of the z-distribution.
A random sample of 10 employees of a company was selected to estimate the mean one-way commute time for all employees at the company. The mean and standard deviation of the sample were 38 minutes and 6 minutes, respectively. Assuming all conditions for inference are met, which of the following is the margin of error, in minutes, for a 95 percent confidence interval for the population mean one-way commute time?
2.262(106)
The manager of a car company will select a random sample of its customers to create a 90 percent confidence interval to estimate the proportion of its customers who have children. Of the following, which is the smallest sample size that will result in a margin of error of no more than 6 percentage points?
200
Researchers investigating a new drug selected a random sample of 200 people who are taking the drug. Of those selected, 76 indicated they were experiencing side effects from the drug. If 5,000 people took the drug, which of the following is closest to the interval estimate of the number of people who would indicate they were experiencing side effects from the drug at a 90 percent level of confidence?
(1620, 2180)
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 cholesterol level, in mg/dl. of all patients of the medical center who had a heart attack in the previous year?
(246.24, 283.16)
The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car?
0.03±2.576500(0.03)(0.97)
A large-sample 98 percent confidence interval for the proportion of hotel reservations that are canceled on the intended arrival day is (0.048, 0.112). What is the point estimate for the proportion of hotel reservations that are canceled on the intended arrival day from which this interval was constructed?
0.080
In 2009 a survey of Internet usage found that 79 percent of adults age 18 years and older in the United States use the Internet. A broadband company believes that the percent is greater now than it was in 2009 and will conduct a survey. The company plans to construct a 98 percent confidence interval to estimate the current percent and wants the margin of error to be no more than 2.5 percentage points. Assuming that at least 79 percent of adults use the Internet, which of the following should be used to find the sample size (n) needed?
2.33n(0.79)(0.21))≤0.025
A random sample of 432 voters revealed that 100 are in favor of a certain bond issue. A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is
0.231±1.964320.231(0.769)
A random sample of 80 people was selected, and 22 of the selected people indicated that it would be a good idea to eliminate the penny from circulation. What is the 99 percent confidence interval constructed from the sample proportion p̂?
0.275±2.57680(0.275)(0.725)
Jessica wanted to determine if the proportion of males for a certain species of laboratory animal is less than 0.5. She was given access to appropriate records that contained information on 12,000 live births for the species. To construct a 95 percent confidence interval, she selected a simple random sample of 100 births from the records and found that 31 births were male. Based on the study, which of the following expressions is an approximate 95 percent confidence interval estimate for p, the proportion of males in the 12,000 live births?
0.31±1.9612,000(0.31)(0.69)
From a random sample of 1,005 adults in the United States, it was found that 32 percent own an e-reader. Which of the following is the appropriate 90 percent confidence interval to estimate the proportion of all adults in the United States who own an e-reader?
0.32±1.6451,005(0.32)(0.68) no square root
A random sample of 300 students is selected from a large group of students who use a computer-equipped classroom on a regular basis. Occasionally, students leave their USB drive in a computer. Of the 300 students questioned, 180 said that they write their name on their USB drive. Which of the following is a 98 percent confidence interval for the proportion of all students using the classroom who write their name on their USB drive?
0.6±2.33300(0.4)(0.6)
A random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council. The table shows the responses by level of support. Based on the responses, which of the following is a 95 percent confidence interval for the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal?
0.71±0.028
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 ?
133
A 95 percent confidence interval of the form p̂ ± E will be used to obtain an estimate for an unknown population proportion p. If p̂ is the sample proportion and E is the margin of error, which of the following is the smallest sample size that will guarantee a margin of error of at most 0.08?
175
A polling agency reported that 66 percent of adults living in the United States were satisfied with their health care plans. The estimate was taken from a random sample of 1,542 adults living in the United States, and the 95 percent confidence interval for the population proportion was calculated as (0.636, 0.684). Which of the following statements is a correct interpretation of the 95 percent confidence level?
Approximately 95% of random samples of the same size from the population will result in a confidence interval that includes the proportion of all adults living in the United States who are satisfied with their health care plans.
A certain county has 1,000 farms. Corn is grown on 100 of these farms but on none of the others. In order to estimate the total farm acreage of corn for the country, two plans are proposed. Plan I: Sample 20 farms at random. Estimate the mean acreage of corn per farm in a confidence interval. Multiply both ends of the interval by 1,000 to get an interval estimate of the total. Plan II: Identify the 100 corn-growing farms. Sample 20 corn-growing farms at random. Estimate the mean acreage of corn for corn-growing farms in a confidence interval. Multiply both ends of the interval by 100 to get an interval estimate of the total. On the basis of the information given, which of the following is the better method for estimating the total farm acreage of corn for the county?
Choose plan II over plan I.
Ten students were randomly selected from a high school to take part in a program designed to raise their reading comprehension. Each student took a test before and after completing the program. The mean of the differences between the score after the program and the score before the program is 16. It was decided that all students in the school would take part in this program during the next school year. Let µA denote the mean score after the program and µB denote the mean score before the program for all students in the school. The 95 percent confidence interval estimate of the true mean difference for all students in the school is (9, 23). Which of the following statements is a correct interpretation of this confidence interval?
For any µA and µB with 9 < ( µA - µB) < 23, the sample result is quite likely.
A manufacturer of piston rings for automobile engines frequently tests the width of the rings for quality control. Last week, a random sample of 15 rings were measured, and the mean and standard deviation of the sample were used to construct a 95 percent confidence interval for the population mean width of the rings. When all other things remain the same, which of the following conditions would have resulted in a wider interval than the one constructed? I. A sample size of 20 with 95 percent confidence II. A sample size of 15 with 99 percent confidence III. A sample size of 12 with 95 percent confidence
II and III only
A researcher constructed a 95 percent confidence interval for the mean number of alfalfa weevils on an alfalfa plant within a field. Based on 80 randomly selected alfalfa plants, the researcher found an average of 2.5 alfalfa weevils per plant and computed the 95 percent confidence interval to be 1.50 to 3.50. Which of the following statements is a correct interpretation of the 95 percent confidence level?
If we repeatedly sampled this field, taking samples of 80 plants and constructing 95% confidence intervals, then, approximately 95 percent of these intervals would include the population mean number of alfalfa weevils on an alfalfa plant in this field.
Monthly rent was determined for each apartment in a random sample of 100 apartments. The sample mean was $820 and the sample standard deviation was $25. An approximate 95 percent confidence interval for the true mean monthly rent for the population of apartments from which this sample was selected is ($815, $825). Which of the following statements is a correct interpretation of the 95 percent confidence level?
In repeated sampling, the method produces intervals that include the population mean approximately 95 percent of the time.
The National Honor Society at Central High School plans to sample a random group of 100 seniors from all high schools in the state in which Central High School is located to determine the average number of hours per week spent on homework. A 95 percent confidence interval for the mean number of hours spent on homework will then be constructed using the sample data. Before selecting the sample, the National Honor Society decides that it wants to decrease the margin of error. Which of the following is the best way to decrease the margin of error?
Increase the sample size
A recent survey estimated that 19 percent of all people living in a certain region regularly use sunscreen when going outdoors. The margin of error for the estimate was 1 percentage point. Based on the estimate and the margin of error, which of the following is an appropriate conclusion?
It is plausible that the percent of all people living in the region who regularly use sunscreen is 18.5%.
A city planner wants to estimate the proportion of city residents who commute to work by subway each day. A random sample of 30 city residents was selected, and 28 of those selected indicated that they rode the subway to work. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?
No, because the sample is not large enough to satisfy the normality conditions.
A local arts council has 200 members. The council president wanted to estimate the percent of its members who have had experience in writing grants. The president randomly selected 30 members and surveyed the selected members on their grant-writing experience. Of the 30 selected members, 12 indicated that they did have the experience. Have the conditions for inference with a one-sample z-interval been met?
No, because the sample size is not less than 10 percent of the population size.
A school librarian wanted to estimate the proportion of students in the school who had read a certain book. The librarian sampled 50 students from the senior English classes, and 35 of the students in the sample had read the book. Have the conditions for creating a confidence interval for the population proportion been met?
No, because the sample was not selected using a random method.
The director of fitness for a large corporation with over 5,000 employees recorded the resting heart rate, in beats per minute (bpm), for 35 employees who were known to wear activity trackers. The following boxplot summarizes the results. The director wants to estimate the resting heart rate for all employees with a confidence interval. Have all conditions for inference been met?
No, the sample was not selected at random.
Animal scientists studied foraging behavior of the scrub lizard, found in central Florida. Foraging is the process of searching for food. To study such behavior, the scientists recorded the number of head movements per minute for a sample of 63 lizards. A 95 percent confidence interval constructed from the sample is given as 2.7±0.622.7±0.62 head movements per minute. Based on the interval, is a claim of 3 head movements per minute plausible?
The claim is plausible because 3 head movements per minute is contained within the interval.
Researchers at a medical center studied the amount of caffeine, in milligrams (mg), contained in a 16-ounce cup of coffee made at one machine at the center's cafeteria. They selected a random sample of 40 16-ounce cups of coffee made at different times of the day during a one-month period. The mean and standard deviation of the amount of caffeine in the sample were 159.88 mg and 36.72 mg, respectively. A graph of the sample data revealed a right skew with one outlier. The researchers will construct a confidence interval to estimate the amount of caffeine for all 16-ounce cups made at the machine. Which of the following conditions is not needed for the inference?
The graph of the sample data is symmetric with no outliers.
Researchers are investigating the effectiveness of leg-strength training on cycling performance. A sample of 7 men will be selected to participate in a training program that lasts for one month. Peak power during cycling will be recorded for each man both before training and after training. The mean difference in times will be used to construct a 95 percent confidence interval for the mean difference in the population. When all other things remain the same, which of the following statements about the width of the interval is correct?
The interval will be narrower if 15 men are used in the sample.
Porcupines can cause damage to wood structures by chewing them. Researchers studied a liquid repellent designed to reduce such damage. A sample of 20 wooden blocks of the same size were treated with the repellent and left outside in an area where porcupines are known to live. After a certain amount of time, the blocks were inspected for the number of porcupine teeth marks visible. The data were used to create the 95 percent confidence interval (4.9, 5.8). Which of the following claims is supported by the interval?
The mean number of porcupine teeth marks on all wooden blocks treated with the repellent is less than 6.
From a random sample of potential voters in an upcoming election, 47% indicated they intended to vote for Candidate R. A 95 percent confidence interval was constructed from the sample, and the margin of error for the estimate was 5%. Which of the following is the best interpretation of the interval?
We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%.
A statistician proposed a new method for constructing a 90 percent confidence interval to estimate the median of assessed home values for homes in a large community. To test the method, the statistician will conduct a simulation by selecting 10,000 random samples of the same size from the population. For each sample, a confidence interval will be constructed using the new method. If the confidence level associated with the new method is actually 90 percent, which of the following will be captured by approximately 9,000 of the confidence intervals constructed from the simulation?
The population median
A school administrator is interested in estimating the proportion of students in the district who participate in community service activities. From a random sample of 100 students in the district, the administrator will construct a 99 percent confidence interval for the proportion of all district students who participate in community service activities. Which of the following statements must be true?
The probability that the confidence interval will include the population proportion is 0.99.
A biologist studying trees constructed the confidence interval (0.14, 0.20) to estimate the proportion of trees in a large forest that are dead but still standing. Using the same confidence level, the interval was later revised because the sample proportion had been miscalculated. The correct sample proportion was 0.27. Which of the following statements about the revised interval based on the correct sample proportion is true?
The revised interval is wider than the original interval because the correct sample proportion is closer to 0.5 than the miscalculated proportion is.
Two random samples, A and B, were selected from the same population to estimate the population mean. For each sample, the mean, standard deviation, and margin of error for a 95 percent confidence interval for the population mean are shown in the table. Which of the following could explain why the margin of error of sample A is greater than the margin of error of sample B?
The sample size of A is less than the sample size of B.
A 90 percent confidence interval is to be created to estimate the proportion of television viewers in a certain area who favor moving the broadcast of the late weeknight news to an hour earlier than it is currently. Initially, the confidence interval will be created using a simple random sample of 9,000 viewers in the area. Assuming that the sample proportion does not change, what would be the relationship between the width of the original confidence interval and the width of a second 90 percent confidence interval that is created based on a sample of only 1,000 viewers in the area?
The second confidence interval would be 3 times as wide as the original confidence interval.
A botanist collected one leaf at random from each of 10 randomly selected mature maple trees of the same species. The mean and the standard deviation of the surface areas for the 10 leaves in the sample were computed. Assume the distribution of surface areas of maple leaves is normal. What is the appropriate method for constructing a one-sample confidence interval to estimate the population mean surface area of the species of maple leaves, and why is the method appropriate?
The t-interval is appropriate, because the population standard deviation is not known.
To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63±±$17.64 Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?
We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.
A random sample of 1,175 people in a certain country were asked whether they thought climate change was a problem. The sample proportion of those who think climate change is a problem was calculated, and a 95 percent confidence interval was constructed as (0.146, 0.214). Which of the following is a correct interpretation of the interval?
We are 95 percent confident that the proportion of all people in the country who think climate change is a problem is between 0.146 and 0.214.
A 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8, 12.3). Which of the following is the best interpretation of the interval?
We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes.
The president of a large company recommends that employees perform, on average, 24 hours of community service each year. The president believes that the mean number of hours of community service performed last year was different from the recommended 24 hours. To estimate the mean number of hours of community service performed last year, the president obtained data from a random sample of employees and used the data to construct the 95 percent confidence interval (20.37, 23.49). If all conditions for inference were met, does the interval provide convincing statistical evidence, at a level of significance of α=0.05.α=0.05. to support the president's belief that the mean number of hours of community service performed last year is different from what is recommended?
Yes, the interval supports the president's belief because 24 is not contained in the interval.
Courtney has constructed a cricket out of paper and rubber bands. According to the instructions for making the cricket, when it jumps it will land on its feet half of the time and on its back the other half of the time. In the first 50 jumps, Courtney's cricket landed on its feet 35 times. In the next 10 jumps, it landed on its feet only twice. Based on this experience, Courtney can conclude that
a confidence interval for estimating the cricket's true probability of landing on its feet is more narrow after the final 10 jumps than it was before the final 10 jumps
When using a one-sample t-procedure to construct a confidence interval for the mean of a finite population, a condition is that the population size be at least 10 times the sample size. The reason for the condition is to ensure that
the degree of dependence among observations is negligible
