Statistics-Final Questions

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 for 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 25% 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

First year students enrolled at a college were asked whether they play video games. The responses, classified by whether the students were enrolled in the school of sciences or the school of arts, are shown in the table. Of all the students enrolled in the school of arts who responded, approximately what proportion responded that they play video games?

0.438

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 selected will be someone who responded no, given that the person selected is age 55 or older?

0.818

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 a Galapagos Islands giant tortoise at the 90th percentile of the distribution?

120 years.

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 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 certain breed of dog's growth during the first year of life can be summarized by the least squares regression line: y-hat=10+1.2x, where x= the age in months y= the weight in pounds What would be the predicted increase in weight for a 5 month old puppy?

16

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

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

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?

50, 20, 70 100, 40, 140 150, 60, 210

The distribution of assembly times required to assemble a certain smartphone is approximately normal with mean 4.6 minutes and standard deviation 0.6 minutes. Of the following, which is closest to the percentage of assembly times between 4 and 5 minutes?

59%

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 currently in stock along with each item's 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.

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 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 teach athletic ability level. Which of the following is the best description of the study?

A randomized block design

The transportation department of a large city wants to estimate the proportion of residents who would use a system of aerial gondolas to commute to work. The gondolas would be part of the city's effort to relieve traffic congestion. The department asked a random sample of residents whether they would use the gondolas. The residents could respond with yes, no, or maybe. Which of the following is the best description of the method for data collection used by the department?

A sample survey

A school committee is lobbying for an increase in the sales tax to support the county school system. The local newspaper conducted a survey of county residents to assess their support for such an increase. What is the population of interest here?

All county residents

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 medicine. A random sample of 500 participants who experience migraines was selected, and the participants were randomly assigned to one of two groups of equal size. The first group received the current medicine and the second group received the new medicine. When a participant experienced a migraine, he or she was instructed to take the medicine and, 15 minutes after taking the medicine, to rate the pain relief on a scale of 1 to 10, with 1 being no relief to 10 being complete relief. At the end of six months, the average pain relief for each participant was calculated. Which of the following is the best description of the study?

An experiment using a completely randomized 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.

Professor James gave the same test to his three sections of statistics students. On the 35-question test, the highest sore was 32 and the lowest was 15. Based on the information displayed in the boxplots above, which of the following statements is true?

At least 50% of the scores in section 3 are higher than all of the scores in section 1.

A mathematics teacher recorded data from her students on how much they studied for their last exam. The teacher then plotted the study times values against the student's test scores. A scatterplot of the data is shown below. Which labeled point on the scatterplot would be considered an outlier?

B.

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.

Bimodal with a gap

Which of the following histograms could have been constructed from the same set of data summarized by the box plot above?

D.

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 distinguishes an observational study from a randomized experiment?

In an observational study treatments are not randomly assigned, whereas in a randomized experiment treatments are randomly assigned.

According to a report for veterinarians in the United States, 36.5 percent of households in the United States own dogs and 30.4 percent of households in the United States own cats. If one household in the United States is selected at random, what is the probability that the selected household will own a dog or a cat?

Not enough information is given to determine the probability

The student government association at a university is interested in the student body's opinions on a docket of topics. The leaders go about this by taking a survey and would like to take a simple random sample of 300 students. Which of the following methods will produce a simple random sample?

Number the students in the official university enrollment records. Use a table of random numbers to choose 300 students from the records for the survey.

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 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.

As 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

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.

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

A school is having a contest in which students guess the number of candies in a jar. The student whose guess is closest to the correct number of candies in the jar wins a prize. The number of candies guessed by male and female students is shown in the back-to-back stemplot below. Which of the following statements is true about the distribution of guesses?

The distribution of guesses for male and female students are both skewed to the left.

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.

The height increases, on average, by 0.48 meters each year.

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.

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

The standard deviation of data set A is greater than the standard deviation of data set B.

After a baby is born, doctors take routine measurements of three different statistics: height, weight, and head size. A pediatrician wonders if there is an association between height and head size. She collects data from the next 20 babies she examines and finds a correlation of 0.82. Interpret this value in context of this problem.

There is a strong, positive, linear association between height and head size.

For which of the following purposes would it be most unreasonable to use a census?

To determine the proportion of red snappers with a high mercury level in the Gulf of Mexico.

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.

Which of the following shapes is not represented by one of the four distributions?

Uniform