Stats final exam study guide

According to loyalty card data, the amount of money spent per shopper at the grocery store is normally distributed with a mean of $75 per trip and a standard deviation of $25 per trip. How much money does a shopper spend that is at the 95th percentile of this distribution?

$116.12

A fish store employee recorded the number of babies born to each of 20 different fish. The data and summary statistics are shown below. If the employee were to randomly select one of these fish, what is the probability that it would have had fewer than 15 babies?

0.2

A random variable X has the following distribution: What is the expected value of X?

0.6

Which of the following scenarios describes an experiment?

A teacher plays classical music while her students take a test to determine if it will increase scores compared to the last test.

A curious accountant at a large firm would like to know if money can buy happiness. She selects a random sample of 30 of her wealthy clients and contacted them to ask "On a scale of 1-100, how happy are you?" The resulting 95 percent confidence interval for the true mean happiness rating for all wealthy customers is (67.5, 89.5). Which of the following statements best summarizes the meaning of 95% confidence?

About 95% of all random samples of 30 wealthy customers from this population would result in a 95 percent confidence interval that captures the population mean happiness rating.

A coin is weighted so that the probability of heads (H) is greater than the probability of tails (T). Which of the following orders is the most probable?

HHH

An organization that strives to hold agencies accountable for truth in news reporting plans to select a random sample of 100 news stories from major U.S. news agencies in order to estimate the proportion of news stories produced by major U.S. news agencies that contain false information. A 90 percent confidence interval for the proportion of all news stories that contain false information will then be constructed. Before selecting the sample, the organization determines that they want to make the margin of error as small as possible. Which of the following is the best way for them to decrease the margin of error?

Increase the sample size.

Lindsey is an avid tennis player. She kept track of the number of winners she had per game for an entire season. The shape of the distribution of the number of winners is roughly symmetric and the five-number summary of the number of winners is: Min: 10 Q1: 18 Med: 48 Q3: 79 Max: 92 Luke is Lindsey's biggest rival. The average number of winners Luke had per game for the season has the same value as Lindsey's IQR. Who had the greatest average number of winners this season? Explain.

Luke, he averaged 61 winners per game while Lindsey only averaged approximately 48 winners per game.

All day laborers of a large manufacturing company receive a 2% raise every 6 months. The current mean hourly wage earned by the all day laborers is $9.75 per hour and the standard deviation of their hourly wages is $0.87 per hour. Assuming that the raise rate and frequency remain the same, what will the mean and standard deviation of the hourly wages earned by day laborers be 2 years from now?

Mean = $10.55, Standard deviation = $0.94

A game show producer asked 100 randomly selected adults, "Have you ever bungee jumped?" Of the adults surveyed, 14 said "Yes!" Is there convincing statistical evidence that the true proportion of all adults that have bungee jumped is more than 10%?

No, because the probability of observing a sample proportion at least as large as 0.14, if the population proportion is 0.10, is greater than 0.05.

Sam is thinking about switching cell phone providers. Sam is particularly interested in making sure that he has good signal strength when he is at work. He asks each of his 30 coworkers what cell phone provider they use and if they have poor signal strength, moderate signal strength, or good signal strength at work. Here is a segmented bar chart of the results. Which of the following statements is supported by the data?

Provider A has reports of the greatest signal strength.

A manager of a local fast food restaurant wants to determine the average amount of time it takes from when a customer enters the drive-through line until they receive their order, regardless of the time of the day and the day of the week. That is, he would like to know the true average drive-through wait time for all his customers. Which of the following methods would be most likely to estimate the desired parameter with low bias and low variability?

Select a random sample of 500 customers over a period of one month, determine each selected customer's wait time, then compute the average wait time for all 500 customers.

An auditor has been assigned the task of inspecting the dice used in a local gaming resort. A fair die shows a 6 face up one-sixth of the time. In order to determine if a die for a particular game is fair, he must observe a long number of trials and record the proportion of the time that the die lands showing a 6 facing up. The graph below shows the cumulative proportion of sixes that are rolled for 100 consecutive trials of a particular game. Which of the following statements is false?

This die appears to be fair because the proportion of sixes fluctuates greatly.

According to a report, more and more young adults are drinking coffee daily. An independent study conducted using a random sample of 500 young adults produces a 95 percent confidence interval for p, the proportion of all young adults who drink coffee daily. The interval was reported to be (0.14, 0.18). Which of the following is correct?

We can be 95% confident that the true proportion of young adults that drink coffee daily is between 0.14 and 0.18.

The author of an article about procrastination in the workplace claimed that, on average, employees waste 2 hours per day surfing the Internet, texting, and e-mailing friends during work hours. Suppose the CEO of a large company wants to determine whether the mean wasted time during an 8-hour work day for employees of her company is less than the mean of 120 minutes reported in the article. She selects a random sample of 10 employees from the company. Each of the 10 employees was called into the CEO's office and she asked them to estimate how much time (in minutes) they typically wasted per day while at work surfing the internet, texting, and emailing friends. The estimate of the amount of time wasted by employees at this company is

likely to be an underestimate of the truth because of response bias.

Ann desires to grow tall sunflower plants. She wonders how the amount of water she provides the sunflowers will affect their growth. One spring Ann planted 25 sunflower plants, making sure each one had the same soil, amount of space, and exposure to sunlight. The first one received one ounce of water per day. The second one received 2 ounces of water per day, and so on. To determine the ideal amount of water needed, she consistently watered her sunflowers this way and at the end of the summer recorded the height of each sunflower (in cm). Then she performed a regression analysis on the data. She conducts a significance test to determine if there is convincing evidence of a positive linear relationship between the amount of water her sunflower plants received and how tall they grew. What is the correct test statistic and conclusion? Assume all conditions for inference are met.

t=2.68. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.

James suspects that, for his place of employment, there is an association between gender and the type of vehicle the person drives. To investigate, he obtains a list of all 641 employees from the business office then selects and surveys a simple random sample of 50 employees. He records the gender of each of the selected individuals as well as whether they drive a car, SUV, or pickup truck. The results are shown in the table. James performs an appropriate significance test to assess the evidence for his claim. Which of the following gives the correct test statistic and p-value?

χ^2=6.61, p-value = 0.0366

In the popular movie, "Back to the Future" Dr. Emmett Brown told Marty McFly, "Don't worry. As long as you hit that wire with the connecting hook at precisely 88 miles per hour the instant the lightning strikes the tower...everything will be fine." Assume the probability that Marty hits the wire with the connecting hook is 0.8. Given that he hits the wire with the connecting hook, the probability that he does so at precisely 88 miles per hour is 0.10. Given that he hits the wire at precisely 88 miles per hour, the probability that this all happens the instant the lightning strikes the tower is 0.02. What is the probability that "everything will be fine"?

0.0016

There are forty multiple-choice questions on this exam, each having answer choices A, B, C, D, or E. Only one answer choice per question is correct. Suppose a student randomly guesses their answer choice to each question, and their guesses from question to question are independent. Which of the following is the probability that the student guesses at least 12 questions correctly on this portion of the exam?

0.0875

Have you ever run into someone you know when you were far away from home? A random sample of 1000 adults were asked this question. Here are their responses: Based on the responses, which of the following is a 90 percent confidence interval for the proportion of all adults who would respond that they have run into someone they know when they were far away from home?

0.199 ± 0.0208

Sharon is a good student who enjoys statistics. She sets a goal for herself to do well enough compared to her peers so that her standardized score on her Statistics final is equal to her percentile rank (written as a decimal) among her classmates. What goal did she set for herself?

0.78

In a certain region of the United States, the distribution of the number of siblings an individual has is strongly skewed to the right with a mean of 1.8 siblings. Which of the following is a possible value for the median of this distribution?

1

The supply manager at a local ice cream shop claims that 80% of customers prefer chocolate over vanilla. One of the employees believes that is an overstatement. He selects a random sample of 50 customers and found that 30 of them preferred chocolate over vanilla. Which of the following is the appropriate margin of error for a 95 percent confidence interval to estimate the population proportion of all customers that prefer chocolate over vanilla?

1.96 √(0.6)(1−0.6)​​/50

Suppose that the McAllister's purchased 15 plane tickets for an upcoming family trip to Paris. Each ticket independently has a 0.01 probability of being accidentally thrown away. What is the probability that exactly one of the tickets is accidentally thrown away?

15(0.01^{1})(0.99^{14})

Candidate A and Candidate B are running for president. You are planning a survey to determine what proportion of registered voters plan to vote for Candidate A pp. You will contact a random sample of registered voters. You want to estimate pp with 99% confidence and a margin of error no greater than 0.01. What is the minimum number of registered voters you will need to survey in order to meet these requirements?

16,590

The United States Postal Service delivers many packages every day. A postal carrier recorded the number of packages he delivered each day for 92 days. Each day had a unique number of packages delivered (no doubles). Here are the results: Mean: 110 Standard Deviation: 24.25 Q1: 75 Median: 98 Q3: 122 How many days did he deliver fewer than 75 packages?

23

The least-squares regression equation y^​=10+2x describes the relationship between x = age (in weeks) and y = weight (in pounds) for a sample of 50 German shepherd puppies for ages 5 ≤ x ≤ 20 weeks. The weight of a particular German Shepherd puppy that is 10 weeks old is underestimated by 10 pounds. How much does this particular puppy weigh?

40 pounds

A dog breeder would like to know how many Dalmatian puppies are typically born in a litter. He conducts some research and selects a random sample of 101 Dalmatian birth records. He examines each birth record and identifies the number of puppies that were born in the litter. The distribution of the number of puppies born per litter was skewed left with a mean of 6.2 puppies born per litter and a standard deviation of 2.1 puppies per litter. He would like to estimate, with 99% confidence, the mean number of puppies born per litter for all Dalmatian births. Which of the following is the correct interval?

6.2 ± 2.626(0.21)

What is the proper way to install a roll of toilet paper: the "over" position, in which the portion you grab hangs over the top of the roll, or the "under" position, in which the portion you grab hangs under/behind the roll? A curious student investigated this question by asking a random sample of 10 custodians and a random sample of 50 adults that are not custodians. The table summarizes the results: If one of these individuals is randomly selected, what is the probability that they are a custodian, given that they said "over"?

8/40

Which of the following distributions will best be modeled by a normal distribution?

A binomial distribution with n=150 and p=0.5.

Researchers are using a new fitness watch with heart monitoring capabilities to study the human heart. In particular, they are examining the relationship between the presence of arrhythmias, or irregular heartbeats, and stress. A random sample of 100 women between the ages of 30 and 50 were selected for a study. At the beginning of the study, each woman completed a questionnaire that classified them as having high or low stress. Each woman was also given a fitness watch to wear for 1 week. The watches revealed to the researchers whether each woman had a heart arrhythmia. The following table gives the number of women that fall into each category. Based on these data, which of the following conclusions is most appropriate?

Although cause-and-effect cannot be established, there is an association between stress and the presence of heart arrhythmias for the population of all women aged 30 to 50.

Professor Chauvet has 6 snake plants at her home. Two are small, two are medium, and two are large. She wants to see if the plants will grow taller if they are given water from her fish tank. She puts all the plants in her bay window at home so they receive equal amounts of sunlight. For the two small plants, she flips a coin to determine which one will get the water from the fish tank. She does the same for the medium, and large plants. She waters them this way weekly for 10 weeks. After 10 weeks she compares the difference in growth for each set of 2 plants. Which of the following is the best description of the method she is using for data collection?

An experiment with a matched-pairs design

The phrase, household penetration, describes the percentage of households that purchase a particular item. The household penetration for toilet paper is 97%. You survey a random sample of 50 households and want to compute the probability that at least one of the households does not purchase toilet paper. Which of the following is appropriate for modeling this distribution?

Binomial distribution

An epidemiologist was called upon to investigate a case of food poisoning at a company picnic. After interviewing 150 of the attendees, the epidemiologist constructed the following table. Let A be the event that a randomly selected person ate the potato salad. Let B be the event that a randomly selected person got food poisoning. Which of the following statements is correct?

Events A and B are dependent.

A manufacturer of all-in-one printers is concerned that the warranty costs for a particular printer model exceed the amount expected by the company. Based on a review of completed warranty claims, the distribution of the warranty cost per claim is skewed to the right with mean $150 and standard deviation $50. A random sample of 25 completed warranty claims is selected, and the sample mean cost is recorded. Suppose the process of selecting a random sample of 25 completed warranty claims and recording the sample mean cost is repeated for a total of 100 samples. Which of the following best describes a dotplot created from the 100 sample means?

The dotplot is closer to approximately normal than the distribution of the population with mean $150 and standard deviation $10.

A college professor recorded the speed with which students ran out the door after class after taking the final exam (using a radar gun) for each of the last 4 semesters. The histogram below shows the distribution of speed for 168 students. The maximum value is 18 mph. The value, 18 mph, was actually supposed to be 8 mph and this error is corrected. Which of the following is true?

The mean will change more than the median, and the range will change more than the SD.

The American Heart Association randomly selected 100 adult males and emailed them a survey that asked two questions: "Have you ever experienced a heart attack?" and "Are you religious?". Of those that were sent the survey 38 completed the survey. What are the population and the sample of this study?

The population is all adult males, and the sample is the 38 adult males that completed the survey.

A school district determines the mean and the standard deviation of the number of days that students of the district are absent for the last quarter of the school year. Which of the following is the best description of the standard deviation?

The standard deviation gives the approximate mean distance between the mean number of days absent for these students and the number of days absent by the individual students.

A statistics teacher created a homework completion incentive program. If a student completes all of their homework for the entire chapter, their name is written on the board in a numbered list. Then the teacher selects 5 names from the list, without replacement, using a random number generator and awards those students with a homework pass. What type of sample did the teacher select?

a simple random sample from the population of all students that completed the homework

The manager of a landscaping company collected data for an entire summer. Before each job he completely filled the gasoline tank for his mower. After each job, he recorded the square footage of the lawn that was mowed as well as how much gasoline remained in the tank. As expected, larger lawns left him with very little gasoline in the tank. At the end of the season he displayed the data in a scatterplot and saw that the relationship between lawn size and gas remaining was roughly linear. The value of r^{2} was 0.85. Find and interpret the value of the correlation between the lawn size and the amount of gasoline remaining in the tank at the end of the job.

r=−0.92. The linear relationship between lawn size and gas remaining is strong and negative.