stats 8.2 homework

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 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)​​

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)​​ square root one

One way to measure the duration of subterranean disturbances such as earthquakes and mining is to calculate the root-mean-square time. The following histograms summarize the distributions of the root-mean-square times for two sources of disturbances. Based on the histograms, which of the following correctly compares the two distributions?

The median of the earthquake disturbances is less than the median of the mining disturbances.

Data will be collected on the following variables. Which variable can be considered discrete?

The number of books a person finished reading last month

Paul will select a random sample of students to create a 95 percent confidence interval to estimate the proportion of students at his college who have a tattoo. Of the following, which is the smallest sample size that will result in a margin of error of no more than 5 percentage points?

385

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

In a large school district, 16 of 85 randomly selected high school seniors play a varsity sport. In the same district, 19 of 67 randomly selected high school juniors play a varsity sport. A 95 percent confidence interval for the difference between the proportion of high school seniors who play a varsity sport in the school district and high school juniors who play a varsity sport in the school district is to be calculated. What is the standard error of the difference?

0.0695

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)​​

The following histogram summarizes the amount spent on plane tickets to travel home, in dollars, for a group of 30 college students. If the interval size is decreased from $200 to $100, which of the following must remain the same on the new histogram?

The sum of the frequencies

Which of the following questions about cars in a school parking lot will allow for the collection of a set of categorical data?

What are the colors of the cars in the lot?

A news organization conducted a survey about preferred methods for obtaining the news. A random sample of 1,605 adults living in a certain state was selected, and 16.2 percent of the adults in the sample reported that television was their preferred method. Which of the following is an appropriate margin of error for a 90 percent confidence interval to estimate the population proportion of all adults living in the state who would report that television is their preferred method for obtaining the news?

1.6451,605(0.162)(1−0.162)​​

For the three histograms above, which of the following correctly orders the histograms from the one with the smallest proportion of data above its mean to the one with the largest proportion of data above its mean?

J L K

Which of the following statistics is defined as the 50th percentile?

The median

The following boxplot summarizes the heights of a sample of 100 trees growing on a tree farm. Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1.5×IQR rule for outliers, is there evidence to support the claim?

No, because 43 is not greater than (Q3+1.5*IQR)

Athletes in a particular sport are classified as either offense or defense. The distribution of weights for the athletes classified as offense is approximately normal, centered at 200 pounds, and ranges from 150 pounds to 250 pounds. The distribution of weights for the athletes classified as defense is approximately normal, centered at 300 pounds, and ranges from 250 pounds to 350 pounds. There are 1,000 athletes in each classification. Which of the following is the best description of a histogram of the weights of all 2,000 athletes?

Bimodal

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

Data on homes recently sold in a certain town included the area of the home, reported in square feet. The table below shows summary statistics of the reported areas, in square feet. An auditor determined that an error was made in the reported areas and that all of the areas should have been 100 square feet greater than what was reported. The areas were corrected and new summary statistics were reported. What are the interquartile range (IQR) and the standard deviation of the corrected areas?

IQR 102, standard deviation 61.0723

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 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.

Of the following dotplots, which represents the set of data that has the greatest standard deviation?

only on the sides

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

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 child psychologist asked 100 five year olds and 50 ten year olds to name their favorite color. Their results are shown in the following table. RedOrangeYellowGreenBluePurpleFive year olds21158103511Ten year olds72615128 Which of the following statements is supported by the table?

The percentage of five year olds who selected red or blue as their favorite color is greater than the percentage of ten year olds who selected red or blue as their favorite color.

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

The number of hurricanes reaching the East Coast of the United States was recorded for each of the last ten decades by the National Hurricane Center. Summary measures are shown below. Min = 12 Max = 24 Lower quartile = 15 Upper quartile = 18 Median = 16 n = 10 Which of the following statements is true?

24 is an outlier and it is possible that there are other outliers at the high end of the data set. There are no outliers at the low end of the data set.

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 commercial for a breakfast cereal is shown during a certain television program. The manufacturer of the cereal wants to estimate the percent of television viewers who watch the program. The manufacturer wants the estimate to have a margin of error of at most 0.02 at a level of 95 percent confidence. Of the following, which is the smallest sample size that will satisfy the manufacturer's requirements?

2,500

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 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

A newspaper poll found that 52 percent of the respondents in a large random sample of likely voters in a district intend to vote for candidate Smith rather than the opponent. A 95 percent confidence interval for the population proportion was computed to be 0.52\pm0.040.52±0.04. Based on the confidence interval, which of the following should the newspaper report to its readers?

No prediction about who will win can be made with 95% confidence.

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.

New employees at a large corporation go through a training program during their first week of employment. The new employees take a written assessment at the completion of the program to determine how well prepared they are for their jobs. A score greater than the mean indicates a well-prepared employee. Assume the following distributions of new employee scores have the same mean score, the same maximum score, and the same minimum score. Which distribution has a shape that is most likely to represent the greatest percent of well-prepared employees?

The distribution of scores is skewed to the left.

Data were collected on 100 United States coins minted in 2018. Which of the following represents a quantitative variable for the data collected?

The value of the coin

Elly and Drew work together to collect data to estimate the percentage of their classmates who own a particular brand of shoe. Using the same data, Elly will construct a 90 percent confidence interval and Drew will construct a 99 percent confidence interval. Which of the following statements is true?

The width of Elly's interval will be less than the width of Drew's interval.

Based on findings from a recent study on women's health, researchers created a 90 percent confidence interval of (0.42, 0.48) to estimate the percent of all women who do not find time to focus on their own health. Based on the confidence interval, which of the following claims is not supported?

More than 45 percent of all women do not find time to focus on their own health.

The following bar chart shows the relative frequency of days of rain for 30 days in four regions of a certain state. Which of the following statements is not supported by the bar chart?

Region C had more than 25 days of rain.

The prices, in thousands of dollars, of the 35 used cars at a certain car dealership are shown in the table below. Which of the following best describes the shape of the distribution of used car prices at the dealership?

Skewed to the right (positively skewed)

A local real estate magazine used the median instead of the mean when it reported the SAT score of the average student who attends Groveland High School. A graphical display of SAT scores of students who attend Groveland High School indicated that the data were strongly skewed to the right. Which of the following explains why, in this situation, the median is a more accurate indicator of the SAT score of the average student than the mean is?

The mean is affected by the skewness, whereas the median is not.

The figure above summarizes the heights, in centimeters, of approximately 400 pine seedlings six years after they were planted at a center for 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.

The following relative frequency table shows the political party affiliation for a sample of 500 people in a certain town. Political PartyRelative FrequencyDemocrat0.35Republican0.30Independent0.20Green Party0.11Libertarian0.03Other0.01 Which of the following statements is supported by the table?

The number of people affiliated with the Independents is 100.

On the day before an election in a large city, each person in a random sample of 1,000 likely voters is asked which candidate he or she plans to vote for. Of the people in the sample, 55 percent say they will vote for candidate Taylor. A margin of error of 3 percentage points is calculated. Which of the following statements is appropriate?

The sample proportion minus the margin of error is greater than 0.50, which provides evidence that more than half of all likely voters plan to vote for candidate Taylor.

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

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

A survey was conducted to determine what percentage of college seniors would have chosen to attend a different college if they had known then what they know now. In a random sample of 100 seniors, 34 percent indicated that they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who would have attended a different college is

26.2% to 41.8%

Three brands of candy pieces—X, Y, and Z—are made in many colors. Shaela bought one bag of each brand and counted the number of pieces of each color. The graph below shows the relative frequency distribution of colors for each bag. Which of the following statements must be true?

For Brand Y, there were more red candy pieces than green candy pieces in the bag.

Lila and Robert attend different high schools. They will estimate the population percentage of students at their respective schools who have seen a certain movie. Lila and Robert each select a random sample of students from their respective schools and use the data to create a 95 percent confidence interval. Lila's interval is (0.30, 0.35), and Robert's interval is (0.27, 0.34). Which of the following statements can be concluded from the intervals?

Lila's sample size is most likely greater than Robert's sample size.

The following pie chart summarizes the results of a survey given to airlines about the primary reason for flight delays. Which of the following statements is supported by the pie chart?

More delays were caused by weather than by all other reasons combined.

Which of the following describes a continuous variable?

The diameters of the tree trunks at an evergreen farm

USA Today reported that speed skater Bonnie Blair had "won the USA's heart," according to a USA Today/CNN/Gallup poll conducted on the final Thursday of the 1994 Winter Olympics. When asked who was the hero of the Olympics, 65 percent of the respondents chose Blair, who won five gold medals. The poll of 615 adults, done by telephone, had a margin of error of 4 percent. Which of the following statements best describes what is meant by the 4 percent margin of error?

The difference between the sample percentage and the population percentage is likely to be less than 4 percent.

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.

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.

The following frequency table shows the responses from a group of college students who were asked to choose their favorite flavor of ice cream. FlavorFrequencyVanilla100Chocolate65Strawberry35Mint chip45Coffee30Butter pecan25 Which of the following statements is not supported by the table?

One-half of the students chose vanilla or chocolate.

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. Based on the histogram, which of the following is the best description of the distribution?

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.

As part of a community service program, students in three middle school grades (grade 6, grade 7, grade 8) each chose to participate in one of three school-sponsored volunteer activities. The graph below shows the distribution for each class for the three activities. Based on the graph, which statement must be true?

For students in grade 7, the number who chose activity C was greater than the number who chose activity B.

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.

A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each of two random samples selected from the same population: sample R and sample S. Let R represent a random sample of size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal to the point estimate obtained from S, which of the following must be true about the respective margins of error constructed from those samples?

The margin of error for R will be 2 times the margin of error for S.

A marketing company wants to estimate the proportion of consumers in a certain region of the country who would react favorably to a new marketing campaign. Further, the company wants the estimate to have a margin of error of no more than 5 percent with 90 percent confidence. Of the following, which is closest to the minimum number of consumers needed to obtain the estimate with the desired precision?

271

In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequencies of students from each grade who participate in the community service activity. Which of the following statements is supported by the bar chart?

Grade 12 had the least relative frequency of participating students.

A random sample of residents in city J were surveyed about whether they supported raising taxes to increase bus service for the city. From the results, a 95 percent confidence interval was constructed to estimate the proportion of people in the city who support the increase. The interval was (0.46, 0.52). Based on the confidence interval, which of the following claims is supported?

More than 40 percent of the residents support the increase.

A certain motel is roughly 20 miles from the entrance to Yosemite National Park. The motel manager wants to get a better estimate of the distance and asks five people to each measure the distance, to the nearest tenth of a mile, using the odometer in his or her car. The manager will use the median of the five measurements as the estimate of the distance. Which of the following statements is NOT a statistical justification for the manager's plan?

The actual distance should be considered a variable, and taking five measurements allows the manager to estimate the variability in the actual distance.

The following dotplot shows the scores of 25 people who played an online trivia game. Which of the following statements is the best description of the distribution of scores?

The distribution is skewed right.

Which of the following statements must be true about the data sets A and B displayed in the histograms above?

The mean of data set A is equal to the mean of data set B.

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

The pulse rate for each person in a sample of 20 men and 20 women was recorded. The boxplots below summarize the pulse rates for the men and the women in the sample. Which of the following statements about the people in the sample must be true?

At least half of the women had higher pulse rates than three-fourths of the men.

Consider a 90 percent confidence interval for a population proportion p. Which of the following is a correct interpretation of the confidence level 90 percent?

In repeated samplings with the same sample size, approximately 90 percent of the intervals created will capture the population proportion p.

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 recent study on the way that people talk indicated, with 95 percent confidence, that between 35 percent and 41 percent of all adults find the word "whatever" to be the most annoying word in conversation. Based on the confidence interval, which of the following claims is supported?

More than 30 percent of all adults find the word "whatever" to be the most annoying word in conversation.

An environmental group wanted to estimate the proportion of fresh produce sales identified as organic in a local grocery store. In the winter, the group obtained a random sample of sales from the store and used the data to construct the 95 percent z-interval for a proportion (0.087, 0.133 ). Six months later in the summer, the group obtained a second random sample of sales from the store. The second sample was the same size as the first, and the proportion of sales identified as organic was 0.4. How does the 95 percent z-interval for a proportion constructed from the summer sample compare to the winter interval?

The summer interval is wider and has a greater point estimate.

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?

The value of maximum minus third quartile is less than the value of first quartile minus minimum.

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 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.