Cumulative Exam — Cumulative exam Answers

A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher.Based on the 90% confidence interval, (0.02, 0.12), is there convincing evidence that the new formula of laundry detergent is better?

At a local college, an admissions officer surveys the incoming class of 1,000 first-year students concerning their preference of major. The officer randomly selects 100 of them and asks if they intend to major in liberal arts. Of the 100 first-year students, 62 state they intend on majoring in liberal arts. Assuming the conditions for inference have been met, what is the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts?

A 95% confidence interval for the true proportion of teenagers who have been to a professional sporting event is (0.289, 0.416). Is it reasonable to believe that more than 25% of teenagers have been to a professional sporting event?

A large home improvement store is considering expanding its selection of moving products, such as cardboard boxes and packing tape. The store constructs a 90% confidence interval to estimate the proportion of all customers who have moved houses at least once in the last five years. In the random sample of 620 customers, 201 (32.4%) replied that they had moved at least once in the last five years. The sample yielded the 90% confidence interval (0.293, 0.355) for the proportion of all customers who have moved in the past five years. What is the correct interpretation of this confidence interval?

A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15.875, 16.595) ounces. What is the sample mean weight of grapes, and what is the margin of error?

A major car dealership has several stores in a big city. The owner wants to determine if there is a difference in the proportion of SUVs that are sold at stores A and B. The owner gathers the sales records for each store from the past year. A random sample of 55 receipts from store A shows that 30 of the sales were for SUVs. Another random sample of 60 receipts from store B shows that 42 of the sales were for SUVs. Assuming conditions for inference are met, what is the 99% confidence interval for the difference in proportions of sales that are SUVs?Find the z-table here.

In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. The students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. For one student, it lands tails side up six times. The student will construct a 90% confidence interval for the true proportion of tails up. Are the conditions for inference met?

Lighter cars are more fuel-efficient than heavier cars. An environmentalist would like to estimate the true mean weight of all cars. To do so, she selects a random sample of 30 cars and determines the 90% confidence interval for the true mean weight to be 2.8 to 3.4 tons. Which of these statements is a correct interpretation of the confidence level?

An environmentalist would like to estimate the true mean weight of all cars. To do so, she selects a random sample of 30 cars and determines that the 90% confidence interval for the true mean weight to be 2.8 to 3.4 tons. Which of the following would increase the margin of error for this confidence interval?

A store manager wants to estimate the proportion of customers who spend money in this store. How many customers are required for a random sample to obtain a margin of error of at most 0.075 with 80% confidence?Find the z-table here.

A computer company wants to determine the proportion of defective computer chips from a day’s production. A quality control specialist takes a random sample of 100 chips from the day’s production and determines that there were 12 defective chips. He wants to construct a 90% confidence interval for the true proportion of defective chips from the day’s production. Are the conditions for inference met?

What is the z* critical value for constructing a 99% confidence interval for a proportion?Find the z-table here.

A college professor would like to estimate the proportion of students who pull an "all-nighter,” meaning they study all night for an upcoming exam. She selects a random sample of 100 students from her large college and finds that the 99% confidence interval for the true proportion of students who pull an all-nighter is 0.48 to 0.62. Which of these statements is a correct interpretation of the confidence level?

The maker of a cell phone screen protector would like to estimate the proportion of customers who file a warranty claim. To do so, they select a random sample of 200 customers and determine that the 96% confidence interval for the true proportion of customers who file a warranty claim to be 0.15 to 0.28. Which of the following would decrease the margin of error?

After a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. The service department randomly selects 50 cars on the dealership lot, examines them, and determines that 18 have damage. Assuming all conditions have been met, they construct a 99% confidence interval for the true proportion of cars with damage from the storm. What are the calculations for this interval?

What is the z* critical value for constructing a 90% confidence interval for a proportion?Find the z-table here.

An inspector inspects large truckloads of potatoes to determine the proportion with blemishes prior to using the potatoes to make potato chips. She intends to compute a 95% confidence interval for this proportion. To do so, she selects a simple random sample of 90 potatoes, and finds 12 with blemishes. The 95% confidence interval is (0.063, 0.204). What is the correct interpretation for this confidence interval?

According to a recent random survey of 1,963 high school students, 581 report playing a musical instrument. A 90% confidence interval for the population of high school students who play a musical instrument is constructed. Which statement identifies what is being estimated?Find the z-table here.

A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520 apples. If the farmer had selected 160 trees from his large apple orchard rather than 40 trees, what effect would this have had on the margin of error?

A researcher takes a random sample of 2,496 drivers and finds that 1,603 put their phone in "drive mode” to not be distracted while driving. A 90% confidence interval for the proportion of drivers who use "drive mode” on their phones is (0.626, 0.658). Which statement correctly interprets the interval?