1. Height, in meters, is measured for each person in a sample. After the data are collected, all the height measurements are converted from meters to centimeters by multiplying each measurement by 100.Which of the following statistics will remain the same for both units of measure?
(A) The mean of the height measurements
(B) The median of the height measurements
(C) The standard deviation of the height measurements
(D) The maximum of the height measurements
(E) The z-scores of the height measurements
2. A school principal wanted to investigate student opinion about the food served in the school cafeteria. The principal selected at random samples of 50 first-year students, 50 second-year students, 50 third-year students,and 50 fourth-year students to complete a questionnaire. Which of the following best describes the principal’s sampling plan?
(A) A stratified random sample
(B) A simple random sample
(C) A cluster sample
(D) A convenience sample
(E) A systematic sample
3. A candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with mean 720 milligrams (mg).If the manager’s belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights?
(A) 740 mg to 780 mg
(B) 700 mg to 740 mg
(C) 680 mg to 720 mg
(D) 660 mg to 700 mg
(E) 620 mg to 660 mg
4. A company currently uses Brand A lightbulbs, which have a mean life of 1,000 hours. A salesperson marketing Brand B, a new brand of bulb, contacts the company. The company will switch to the new brand of bulb only if there is convincing evidence that the mean life of Brand B is greater than 1,000 hours. Which of the following hypotheses should the company test?
(A)H0 :The mean life of Brand B bulbs is 1,000 hours.
Ha:The mean life of Brand B bulbs is more than 1,000 hours.
(B) H0 :The mean life of Brand B bulbs is 1,000 hours.
Ha:The mean life of Brand B bulbs is less than 1,000 hours.
(C) H0 :The mean life of Brand A bulbs is 1,000 hours.
Ha:The mean life of Brand A bulbs is more than 1,000 hours.
(D) H0 :The mean life of Brand A bulbs is 1,000 hours.
Ha:The mean life of Brand A bulbs is less than 1,000 hours.
(E) H0 :The mean life of Brand A bulbs is equal to the mean life of Brand B bulbs.
Ha:The mean life of Brand A bulbs is not equal to the mean life of Brand B bulbs.
5. The amount of time required for each of 100 mice to navigate through a maze was recorded. The histogram below shows the distribution of times, in seconds, for the 100 mice.Which of the following values is closest to the standard deviation of the 100 times?
(A) 2.5 seconds
(B) 10 seconds
(C) 20 seconds
(D) 50 seconds
(E) 90 seconds
1. A hospital administrator noticed that the first nonemergency surgery scheduled each day often started late. If the first scheduled surgery got delayed, then all of the other surgeries scheduled for that day also got delayed. For three weeks (a total of 15 days) the administrator recorded how many minutes past the scheduled time the first surgery began each weekday. The data are shown in the table below.
The administrator sent a memo to the hospital’s entire surgical staff to ask that everyone work to reduce the delay in the starting time for the first nonemergency surgery each day. The administrator recorded how many minutes past the scheduled starting time the first scheduled surgery began each weekday for the three weeks after the memo was sent out. The data are shown in the table below. A negative number in the table indicates that the surgery started earlier than the scheduled time.
The dotplots below display the distributions of minutes past the scheduled starting time before the memo went out and after the memo went out.
(a) Based only on the dotplots, does it appear that the distribution of minutes past the scheduled starting time changed after the memo was sent? Explain.
(b) The hospital administrator wants to perform a two-sample t-test to determine whether the average number of minutes past the scheduled starting time changed after the memo was sent. State the conditions for that test. For each condition, comment on whether it appears to be met.
2. A certain company makes three grades (A, B, and C) of a particular electrical component. Historically, grade A components have a 2 percent defective rate, grade B components have a 5 percent defective rate, and grade C components have a 10 percent defective rate. Since grade A components are less likely to be defective, the company can charge more money for those components than it can charge for the grade B or C components. Similarly, the company can charge more money for grade B components than it can charge for grade C components.
Recently, the company found a batch of components in a warehouse that were known to be of the same grade, but the grade was not labeled on the components. To determine the grade (A, B, or C), the company selected from that batch a random sample of 200 components, which contained 16 defective components.
(a) Construct and interpret a 95 percent confidence interval for the proportion of defective components in the batch.
If you need more room for your work in part (a), use the space below.
(b) Does the interval calculated in part (a) allow the company to clearly determine the grade of component that was produced in the batch? Explain.