mcq stats final

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. *table* Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the mean cost per customer for the performance?

$29.40

In 1960 sociologists studied a random sample of 1,018 families that consisted of a husband, a wife, and at least one child. Of those families, 5.8 percent reported that the wife was the primary wage earner of the family. In 2011 the study was replicated with a random sample of 1,013 families that consisted of a husband, a wife, and at least one child. Of those families, 22.3 percent reported that the wife was the primary wage earner of the family. Which of the following represents a 99 percent confidence interval for the difference between the proportions of families that consisted of a husband, a wife, and at least one child from 1960 to 2011 that would have reported the wife as the primary wage earner?

(0.223−0.058)±2.576√(0.223)(0.777)/1,013+(0.058)(0.942)/1,018

Data were collected from a longitudinal study designed to investigate the relationship between blood sugar levels and brain shrinkage. The results of an analysis of the data for 22 observations are shown in the table below. *chart* Which of the following represents a 98 percent confidence interval for the slope of the least-squares regression line for brain shrinkage on blood sugar levels? Assume the conditions for inference are met.

0.161 ± 2.528(0.073)

A tropical storm is classified as major if it has sustained winds greater than 110 miles per hour. Based on data from the past two decades, a meteorologist estimated the following percentages about future storms. -20% of all tropical storms will originate in the Atlantic Ocean, of which 20% will be classified as major. -30% of all tropical storms will originate in the eastern Pacific Ocean, of which 15% will be classified as major. -50% of all tropical storms will originate in the western Pacific Ocean, of which 25% will be classified as major. Based on the meteorologist's estimates, approximately what is the probability that a future tropical storm will originate in the Pacific Ocean and be classified as major?

0.170

A survey of a random sample of 1,045 young adults found that 60 percent do not have a landline telephone number. A hypothesis test will be used to determine whether the data provide convincing statistical evidence that more than 50 percent of all young adults do not have a landline telephone number. Which of the following is the test statistic for the appropriate test?

0.60−0.50/√(0.50)(0.50)/1,045

A survey of a random sample of 210 male teens and 228 female teens, ages 13 years to 17 years, found that 122 of the male teens and 160 of the female teens brush their teeth at least twice a day. If there is no difference between the proportions in the population of all male and female teens ages 13 years to 17 years who brush their teeth at least twice a day, approximately how many males and females in the sample would be expected to brush their teeth at least twice a day?

135 males and 147 females

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 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

At a certain store, the distribution of weights of cartons of large eggs is approximately normal with mean 26 ounces (oz). Based on the distribution, which of the following intervals will contain the greatest proportion of cartons of large eggs at the store?

24 oz to 28 oz

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(1.53)

The distribution of weights of female college cross-country runners is approximately normal with mean 122 pounds and standard deviation 8 pounds. Which of the following is closest to the percent of the runners who weigh between 114 pounds and 138 pounds?

82%

Research indicates that the standard deviation of typical human body temperature is 0.4 degree Celsius (C). Which of the following represents the standard deviation of typical human body temperature in degrees Fahrenheit (F), where F=9/5C+32?

9/5(0.4)

Researchers used two footballs of the same size to examine the effect of helium on kicking distance. One football was filled with air, and the other was filled with helium. Eleven people participated in the study. Each person kicked the football filled with air and the football filled with helium, and the kicking distances, in yards, were recorded. The football that was kicked first was determined by the flip of a fair coin, and the people did not know which football was filled with air and which was filled with helium. What type of study was conducted by the researchers and, of the following, which is the appropriate t-interval for inference?

A matched-pairs design and a t-interval for a mean difference

A study was conducted to evaluate the impact of taking a nutritional supplement on a person's reaction time. One hundred volunteers were placed into one of three groups according to their athletic ability: low, moderate, or high. Participants in each group were randomly assigned to take either the nutritional supplement or a placebo for six weeks. At the end of the six weeks, participants were given a coordination task. The reaction time in completing the task was recorded for each participant. The study compared the reaction times between those taking the supplement and those taking the placebo within each athletic ability level. Which of the following is the best description of the study?

A randomized block design

Measurements of water quality were taken from a river downstream from an abandoned chemical dumpsite. Concentrations of a certain chemical were obtained from 9 measurements taken at the surface of the water, 9 measurements taken at mid-depth of the water, and 9 measurements taken at the bottom of the water. What type of study was conducted, and what is the response variable of the study?

An observational study was conducted, and the response variable is the concentration of the chemical.

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 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. One month after they completed the program, the participants were contacted and surveyed about the program. Over 90 percent of the participants claimed they were cured of their fear of spiders. 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.

Researchers investigated whether a new process for producing yarn could reduce the mean amount of volatile organic compounds (VOCs) emitted by carpet. From random samples of carpets, the researchers found the mean reduction of VOCs emitted by carpets made with yarn produced by the new process compared with that of carpets made with yarn produced by the traditional process was 13 parts per million (ppm). All conditions for inference were met, and the p-value for the appropriate hypothesis test was 0.095. Which of the following statements is the best interpretation of the p-value?

If the null hypothesis is true, the probability of observing a mean reduction of at least 13 ppm is 0.095.

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. *boxplot* 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.

A survey was conducted in a large city to investigate public opinion on banning the use of trans fats in restaurant cooking. A random sample of 230 city residents with school-age children was selected, and another random sample of 341 city residents without school-age children was also selected. Of those with school-age children, 94 opposed the banning of trans fats, and of those without school-age children, 147 opposed the banning of trans fats. An appropriate hypothesis test was conducted to investigate whether there was a difference between the two groups of residents in their opposition to the banning of trans fats. Is there convincing statistical evidence of a difference between the two population proportions at the significance level of 0.05 ?

No, because the probability of observing a difference at least as large as the sample difference, if the two population proportions are the same, is greater than 0.05.

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

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.

An airline recorded the number of on-time arrivals for a sample of 100 flights each day. The boxplot below summarizes the recorded data for one year. *box and whisker* Based on the boxplot, which of the following statements must be true?

The difference between the median and the lower quartile for the number of on-time arrivals is less than 2.

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. *histogram* 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.

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?

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

In a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played. The means and standard deviations of the random variables for a particular player are shown in the table below. *table* Assume that X and Y are independent. What are the expected value and the standard deviation of the points per game for the player?

The expected value is -6.5, and the standard deviation is 65.4.

An agricultural scientist wanted to compare the effect of a new fertilizer to that of three older fertilizers—X, Y, and Z—on the growth of vegetables typically grown in small gardens. Two hundred green bean seedlings were individually planted in identical pots and randomly assigned to one of four groups of 50 each. Seedlings in one group were given the new fertilizer, and the three remaining groups of seedlings were given fertilizers X, Y, or Z, respectively. At the end of four weeks, all seedlings were dried and weighed. The scientist found that the mean weight of the seedlings in the group given the new fertilizer was significantly greater than the mean weights of seedlings in the other three groups. The scientist concluded that the new fertilizer was more effective than the other fertilizers for all vegetables. Why is the scientist's conclusion not appropriate?

The experiment only included green beans, so the results cannot be generalized to all vegetables.

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.

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.

In a physics experiment, two different methods were used to measure the angle of deflection when a subatomic particle collides with a certain material. Ten specimens of the material were used to compare the two methods. For each specimen, the angle of deflection was measured using both methods. For each specimen, the method used first was determined by the flip of a fair coin. The difference between the measured angles was calculated for each specimen. A test of the hypothesis that the population mean difference is zero had a p-value of 0.082. The hypothesis test described had three components: the number of specimens, the sample standard deviation of the differences, and the magnitude of the sample mean difference. Compared to the test described, which of the following would have resulted in a smaller p-value?

The number of specimens remained the same, but the magnitude of the sample mean difference was larger and the sample standard deviation of the difference was smaller.

A two-sided t-test for a population mean is conducted of the null hypothesis H0 : μ = 100. If a 90 percent t-interval constructed from the same sample data contains the value of 100, which of the following can be concluded about the test at a significance level of a = 0.10 ?

The p-value is greater than 0.10, and H0 should not be rejected.

A police officer uses a motion detector to indicate whether a car is traveling faster than the speed limit (speeding). A speeding ticket will be issued to the driver of the car if the officer believes the driver is speeding, as indicated by the detector. The situation is similar to using a null and an alternative hypothesis to decide whether to issue a ticket. The hypotheses can be stated as follows. H0 : The driver is not speeding. Ha : The driver is speeding. Which of the following best describes the power of the test?

The probability of issuing a ticket to a driver who is speeding

Staff members of a high school newspaper want to obtain an estimate of the average number of years teachers in the state have been teaching. At an educational conference attended by many teachers in the state, the staff members randomly selected 50 conference attendees and asked the attendees how long they have been teaching. Which of the following describes the sample and the population to which it would be most reasonable for the staff members to generalize the results?

The sample is the 50 conference attendees, and the population is all conference attendees.

As part of a science experiment, a student recorded 10 measurements of the temperature of a liquid. One of the measurements was an outlier when compared with the other 9 measurements. Which of the following must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements? (Note: An outlier is any number that is greater than the upper quartile or less than the lower quartile by at least 1.5 times the interquartile range.)

The standard deviation of the 9 measurements is less than the standard deviation of the 10 measurements.

Researchers believed that an increase in lean body mass is associated with an increase in maximal oxygen uptake. A scatterplot of the measurements taken from 18 randomly selected college athletes displayed a strong positive linear relationship between the two variables. A significance test for the null hypothesis that the slope of the regression line is 0 versus the alternative that the slope is greater than 0 yielded a p-value of 0.04. Which statement is an appropriate conclusion for the test?

The strong positive linear relationship displayed in the scatterplot along with a p-value less than 0.05 indicates that college athletes with higher lean body mass tend to have higher maximal oxygen uptake.

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.

An experiment was conducted to investigate the relationship between the dose of a pain medication and the number of hours of pain relief. Twenty individuals with chronic pain were randomly assigned to one of five doses—0.0, 0.5, 1.0, 1.5, 2.0—in milligrams (mg) of medication. The results are shown in the scatterplot below. *graph* The data were used to fit a least-squares regression line to predict the number of hours of pain relief for a given dose. Which of the following would be revealed by a plot of the residuals of the regression versus the dose?

The variation in the hours of pain relief is not the same across the doses.

Researchers conducted a telephone survey of 427 adults living in a large city. The adults were asked whether they planned to purchase a smart watch in the next year. The table shows the responses categorized by the region of the city in which the residents live. *table* Which of the following graphical displays is most appropriate for preparing the proportions of those surveyed who plan to purchase a smart watch within the four regions?

a segmented bar chart

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 shows the distribution of responses?

c.) 50 20 70 100 40 140 150 60 210

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. *dot plot* Based on the dotplots, which of the following is greater for the percent moisture of corn than for the percent moisture of soybeans?

the range