Toddlers tend to have an abundance of energy. To put that energy to good use a fitness instructor creates a Toddler Fitness class. In this class the participants have to do everything the fitness instructor’s energetic toddler daughter does. To compare the number of calories burned in Toddler Fitness versus the standard fitness class 40 volunteers are recruited. The volunteers are assigned at random to participate in Toddler Fitness or the standard fitness class. Each participant wears a calorie counting fitness watch. At the end of the class the calories burned by each participant is recorded and the average number of calories burned is calculated for each class. After the classes ended, the instructor learned that the mean number of calories burned by the participants in Toddler Fitness was significantly greater than the mean number of calories burned by the participants in the standard fitness class. Which of the following is the most appropriate conclusion?

There is convincing evidence that Toddler Fitness caused the participants to burn more calories than the standard fitness class, and the conclusion cannot be generalized beyond those in the study

There is convincing evidence that Toddler Fitness caused the participants to burn more calories than the standard fitness class, and the conclusion can be generalized to all adults that workout.

There is convincing evidence that Toddler Fitness caused the participants to burn more calories than the standard fitness class, and the conclusion can be generalized to all students of this fitness instructor

Cause-and-effect cannot be established, but there is an association between the type of exercise class taken and the number of calories burned in the population of all adults that workout.

Cause-and-effect cannot be established, but there is an association between the type of exercise class taken and the number of calories burned in the population of all students of this fitness instructor.

In order to estimate the proportion of students that text while driving, a school administrator selects a simple random sample of students from a list of all students at the school who have parking permits. The students are called to the office, one at a time. The administrator asks each student, “Do you text while driving, even though you are not supposed to?” Based on the survey, the administrator estimates that only 2% of students with parking passes text while driving. What potential bias is present in the design of this survey and what is the likely direction of the bias?

The sample proportion is likely an underestimate of the population proportion due to response bias.

The sample proportion is likely an underestimate of the population proportion due to undercoverage.

The sample proportion is likely an underestimate of the population proportion due to nonresponse.

The sample proportion is likely an overestimate of the population proportion due to response bias.

The sample proportion is likely an overestimate of the population proportion due to undercoverage.

The guidance counselor of a large high school reports that 48.5% of Junior Pre-Calculus students signed up to take AP Statistics next year, 52.5% signed up to take AP Calculus next year and 10% of Junior Pre-Calculus students signed up to take both AP Statistics and AP Calculus next year. If one Junior Pre-Calculus student is selected at random, what is the probability that they did not sign up to take AP Statistics or AP Calculus next year?

Not enough information is given to determine the probability.

An online clothing company decides to investigate whether offering their customers a coupon upon completion of their first purchase will encourage them to make a second purchase. To do so, the company programs the website to randomly select 100 first time customers. Sixty of these customers are randomly selected to receive a coupon for $5 off their next purchase, to be made in the next 30 days. The other 40 customers are not offered a coupon. The table above shows the number of customers in each group that made a second purchase within 30 days of their first purchase. Based upon the table, is “yes, made a second purchase” independent of “yes, being sent a coupon”?

No, the probability of making a second purchase is not equal to the probability of making a second purchase given that a coupon was sent.

Yes, exactly half of the customers made a second purchase and half did not.

Yes, the largest count in the table comes from those who were sent a coupon and made a second purchase within 30 days.

No, the probability of making a second purchase is the same whether or not a coupon was sent.

It is impossible to draw a conclusion about independence because a coupon was not sent to exactly half of the customers.

Students in a statistics class participated in a project in which they attempted to estimate the true mean height of all students in their large high school. The students were split into 4 groups. Each group had their own sampling method, and they used it to select a sample each day for 50 days. Shown above are the estimates based on their 50 samples. A fter the samples were collected and the means were plotted the teacher visited the school nurse who told her that the true mean height of all students in the school is 67.5 inches. Which group produced sample statistics that estimated the true value of the parameter with relatively low bias and low variability?

A ll groups produced statistics that have low bias and low variability because $$\overline{x}$$ is an unbiased estimator of $$\mu$$

A poll was conducted using a sample of 2500 registered voters to determine what proportion of voters are planning to vote for the incumbent president in the upcoming election. The pollsters reported, “We are 95% confident that the true proportion of registered voters that will vote for the incumbent president is within the interval 0.465 to 0.545.” What is meant by 95% confidence?

The pollsters used a method that will capture the true population proportion in about 95% of all possible confidence intervals based upon random samples of size 2500 from this population.

The pollsters used a method that is guaranteed to capture the true voting preference of 95% of the registered voters

The pollsters can be 95% confident that the incumbent president will receive 50.5% of the vote and will win the election.

There is a 95% chance that the interval (0.465, 0.545) contains the true proportion of voters that are planning to vote for the incumbent president.

If the pollsters take many random samples of size 2500 from this population, about 95% of the resulting intervals will contain 0.505.

A cat-lover claims that cats are just as smart as dogs. In order to back this claim up with some evidence she organizes a study at a large local pet daycare center. A random sample of 40 cats are selected and a random sample of 40 dogs are selected. Each of the selected animals is given one hour with a trainer in which the trainer attempts to teach them to roll over. Upon conclusion of the training, the proportion of dogs and proportion of cats that have learned this skill is computed. The trainer reports that she is 90% confident that the true difference in the proportion of all dogs and all cats (pD – pC) that can learn this skill with one hour of training is between –0.05 to 0.28. Which of the following conclusions can be made based upon this confidence interval?

Because 0 is contained in the interval, there is not convincing evidence that the proportion of all dogs that can learn the skill with one hour of training differs from the proportion of all cats that can learn the skill with one hour of training.

Because most of the values in the confidence interval are positive, this proves that dogs are smarter than cats.

Because the point estimate of the confidence interval is positive, there is convincing evidence that the proportion of all dogs that can learn the skill with one hour of training is greater than the proportion of all cats that can learn the skill with one hour of training.

Because 0.115 is contained in the interval, there is not convincing evidence of a difference in the population proportions.

Because the margin of error of the confidence interval is greater than 0.05, there is not convincing evidence that the proportion of all dogs that can learn the skill with one hour of training differs from the proportion of all cats that can learn the skill with one hour of training.

A student would like to estimate the proportion of the senior class that plans to attend prom this year. The student goes to the guidance office and gets a list of the names of all 274 seniors. Using the list, she selects a simple random sample of 50 students and finds that 76% of the selected students plan to attend prom this year. She would like to construct a 95% confidence interval for the proportion of the entire senior class that plans to attend prom this year. Are the conditions for inference met?

No, although the random and large counts conditions are met, the 10% condition is not met.

Yes, all conditions for inference are met.

No, although the random and 10% conditions are met, the large counts condition is not met.

No, there are two conditions for inference that are not met.

No, none of the conditions for inference are met.

Lexie is a waitress. She believes that she earns more tips, on average, when she curls her hair before work rather than pulling it back in a ponytail. In order to investigate this belief, she writes “curls” on 30 slips of paper and “ponytail” on 30 slips of paper, puts them in a hat and mixes them well. Each time she gets ready for work she randomly selects one piece of paper to determine how she should do her hair that day. Using the data she collects, she carries out a t test for a difference in means in order to test the hypotheses shown above where $$\mu$$ C = the mean amount of tips that Lexie would make for all days in which she curls her hair and $$\mu$$ P = the mean amount of tips that Lexie would make for all days in which she pulls her hair up in a ponytail. The P-value of this test is 0.0375. What is the interpretation of this value?

A ssuming the true difference (Curls – Ponytail) in the mean amount of tips received is 0, there is a 0.0375 probability that Lexie would observe a difference in sample means as greater or greater than she did by chance alone.

A ssuming that the true mean amount of tips that Lexie would receive while wearing curls is greater than the true mean amount of tips that Lexie would receive while wearing her hair in a ponytail, there is 0.0375 probability that the null hypothesis would be rejected.

The P-value indicates that there is a probability of 0.0375 that the null hypothesis is true.

Because the P-value is less than $$\alpha$$ = 0.05, Lexie should fail to reject the null hypothesis and interpret the results to mean that she has proven that she makes more money in tips when she curls her hair.

There is a 0.0375 probability that Lexie will make more money in tips when she wears her hair in curls opposed to wearing her hair in a ponytail.

Erica has a swimming pool at her house. Once a year she purchases a 50-pound bucket of chlorine pellets from an online company. Out of curiosity she weighs the bucket and finds that it only weighs 46.2 pounds. She purchases 4 more 50-pound buckets, giving her an SRS of size 5. The mean weight of the 5 buckets is 48.5 pounds. She suspects that the company is cheating the customers. She uses her data to test the hypotheses H0: $$\mu$$ = 50 pounds versus Ha: $$\mu$$ < 50 pounds. The P-value of her test is 0.0851. What decision should she make and what type of error could she make as a result of her decision? Use $$\alpha$$ =0.05

She should fail to reject H0 She could make a Type II error, meaning she fails to find convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is.

She should reject H0. She could make a Type I error, meaning she finds convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is not.

She should reject H0. She could make a Type II error, meaning she fails to find convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is

She should fail to reject H0. She could make a Type I error, meaning she finds convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is not.

She should fail to reject H0. She could make a low power error, meaning that she rejects the null hypothesis when the null hypothesis is true.

A recent study sought to determine if exercising after studying for an exam may help retain information. The 150 student volunteers that participated in the study were randomly assigned to three groups. All students were given a picture memory task that they studied for 15 minutes. After studying, one of the groups was instructed to exercise for 30 minutes immediately after studying. A second group was instructed to wait 1 hour after studying and then exercise for 30 minutes. The third group was instructed to not exercise after studying. The next day all 150 student volunteers were given a test to determine how well they could remember what they studied. Shown above are the results. The researchers want to test: H0: There is no difference in the distribution of performance on the test for the three treatment groups among the population of all student volunteers like these. Ha: There is a difference in the distribution of performance on the test for the three treatment groups among the population of all student volunteers like these. Which test is appropriate in this situation?

chi-square test for homogeneity

chi-square test for association

chi-square test for goodness of fit

Statistics Diagnostic Quiz

1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

A college professor conducted a survey in order to assess how much money nursing majors spend on course material compared to all other majors. To do so, she selected a random sample of 34 students. Each student was classified as a nursing major or as a non-nursing major. They were then asked how much they spent on books and other materials required for their courses this semester. Shown above are parallel boxplots summarizing the responses. Based upon the boxplots, which of the following statements cannot be concluded?

The range of the distribution of the cost of course materials for nursing majors is about the same as that of non-nursing majors.

The maximum cost for non-nursing majors is greater than the median cost for nursing majors.

The variability of the cost of course materials for the middle 50% of nursing majors is greater than the variability of the middle 50% for non-nursing majors.

The median cost of course materials for nursing majors is over $300 more than the median cost of course materials for non-nursing majors.

The boxplots reveal that 17 students are nursing majors and 17 students are non-nursing majors.

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

In order to compare the real estate markets in Pittsburgh and Philadelphia, a realtor selected a random sample of 150 homes in the Pittsburgh area and 100 homes in the Philadelphia area. Shown above are dotplots showing the distribution of home price for the homes in these two cities. The mean home price for both cities is approximately $500,000. The standard deviation of home price for one city is $100,740 and the other is $267,210. Which of the following gives the correct value and interpretation of the standard deviation of the home prices for homes in the Pittsburgh area?

The price of homes in the Pittsburgh sample are within $100,740 of the mean home price of $500,000.

In the sample of homes from Pittsburgh, most of the home prices are at least $100,740 above or below the mean home price of $500,000

The price of the homes in the Pittsburgh sample typically vary by about $267,210 from the mean home price of $500,000.

In the sample of homes from Pittsburgh, the middle 50% of home prices are within $267,210 of the mean home price of $500,000.

The price of homes in the Pittsburgh sample are $100,740 from the mean home price of $500,000

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The segmented bar graph shows how many of the first 44 United States Presidents have died while in office, classified by political party. What proportion of these Presidents have died while in office?

0.045

0.080

0.091

0.182

0.662

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

A grocery store manager wants to estimate the mean purchase total for all customers that shop at her store. To do so, she selects a random sample of 30 receipts from the large list of all receipts that are stored in the computer. Shown above is a dotplot of the results. The mean purchase total is $93.80 and the median purchase total is $75.80. The store manager investigates and learns that the customer that made a $500 purchase had not purchased groceries, but rather a $500 gift card. Because this customer’s purchase was not typical, the manager decides to exclude this total from the data set. How will removing the $500 purchase from the data set affect the value of the mean and the median?

The mean will decrease more than the median.

The mean will decrease less than the median

The mean will stay the same, but the median will decrease

The mean will increase more than the median.

The mean will increase, but not as much as the median.

5.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

When homeowners list their home for sale, they begin by listing it for a price that is greater than what they expect to receive. The longer a home is on the market, without being sold, the more the price drops. A realtor selects 50 homes that are currently listed for sale. A scatterplot reveals that the association between x = the number of days the home is on the market and y = the current asking price ($) is fairly linear and can be modeled by the equation shown above. Additionally, 85.4% of the variation in the current asking price can be explained by this linear model. Which of the following is the value of the correlation (r) for the relationship between x and y?

–200

–0.924

0.146

0.854

0.924

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Active is an energy drink that claims to provide physical strength. To test this claim, the producers of Active conducted a study. The company recruited 25 high school athletes and 4 professional football players to participate in the study. The high school athletes were each randomly assigned to drink between 1 and 5 ounces of Active. The professional football players were assigned to drink either 30 or 31 ounces. After waiting 10 minutes they completed as many pull-ups as they could. Shown above is a scatterplot showing the number of energy drinks consumed and the number of pull ups that were completed by each participant, as well as a line of best fit. Which of the following would increase if the professional football players were removed from the data set?

r

r²

the slope

the standard deviation of the residuals

none of the above

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Certain car manufacturers install a gauge that tells the driver how many miles they can drive until they will run out of gas. A study was conducted to test the accuracy of these gauges. Each driver was assigned a certain gauge reading until empty to watch for. When their car announced it had that many miles remaining until empty, they began to measure their distance traveled. After they ran out of gas, they reported the distance they were able to drive (in miles) as well as the gauge reading they were assigned (in miles). Shown above is computer output showing the regression analysis. Identify and interpret the slope of the regression line used for predicting the actual distance that can be driven based on the gauge reading.

Slope = 1.1889. The predicted distance the drivers were able to drive increases by 1.1889 miles for each additional mile reported by the gauge.

Slope = 0.0457. The predicted distance the drivers were able to drive increases by 0.0457 miles for each additional mile reported by the gauge.

Slope = –0.7928. The predicted distance the drivers were able to drive decreases by 0.7928 miles for each additional mile reported by the gauge.

Slope = 1.1889. For each additional mile reported by the gauge, the drivers were able to drive an additional 1.1889 miles.

Slope = 0.0457. For each additional mile reported by the gauge, the drivers were able to drive an additional 0.0457 miles.

8.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

A well-balanced stock market portfolio will often experience an exponential growth. A particular investor with a well-balanced stock market portfolio records the portfolio balance every month, in thousands of dollars, from the date of investment. The roughly exponential growth can be transformed to a linear model by plotting the natural log of the balances versus time, in months, where t = 0 represents the date the money was invested. The linear regression equation for the transformed data is shown above. Using this equation, what is the predicted balance of the portfolio after 2 years (24 months)?

$5,654

$6,798

$285,431

$896,053

$948,464

9.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

At Central High School, 28% of the students are Freshmen, 26% are Sophomores, 24% are Juniors, and 22% are Seniors. The student manager of the school newspaper would like to conduct a survey to estimate the proportion of each class that plans to attend the upcoming Football game. She suggests surveying a random sample of 100 students, but specifically by selecting random samples of 28 Freshmen, 26 Sophomores, 24 Juniors, and 22 Seniors. Which of the following is a true statement about this sampling procedure?

This is a simple random sample because students of every class have an equal chance of being selected.

This is a cluster random sample because there are 4 groups of students that are to be selected.

This is a convenience sample because only 100 students are surveyed, which is a manageable size.

This is a stratified random sample because a separate random sample is selected from each class

This is a systematic random sample because each class makes up approximately one-fourth of the student body

10.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

A study is conducted to investigate whether customer satisfaction is greater among computer companies that offer tech support versus those that do not offer tech support. A random sample of 50 customers are selected from among those that purchased computers that offer tech support. A separate random sample of 40 customers are selected from among those that purchased computers that do not offer tech support. The study found that the mean satisfaction rating was significantly greater among customers that purchased computers that offer tech support. Which of the following is the best description of this study?

An experiment using a completely randomized design.

An experiment using a randomized block design.

An experiment using a matched pairs design.

An observational study using a simple random sample.

An observational study using a stratified sample

Statistics Diagnostic

30 questions

The segmented bar graph shows how many of the first 44 United States Presidents have died while in office, classified by political party. What proportion of these Presidents have died while in office?

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