Unit 10 Test Warm Up

A university researcher wants to estimate the mean number of novels that seniors read during their time in college. An exit survey was conducted with a random sample of 9 seniors. The sample mean was 7 novels with standard deviation 2.29 novels. Assuming that all conditions for conducting inference have been met, which of the following is a 95 percent confidence interval for the population mean number of novels read by all seniors?

• 7 ± 1.960 (2.29/√8)

• 7 ± 1.960 (2.29/√9)

• 7 ± 2.262 (2.29/√9)

• 7 ± 2.306 (2.29/√8)

• 7 ± 2.306 (2.29/√9)

Answer explanation

Tags

CCSS.HSS.IC.B.4

Of all the fish in a certain river, 20 percent are salmon. Once a year, people can purchase a fishing license that allows them to catch up to 8 fish. Assume each catch is independent. Which of the following represents the probability of needing to catch 8 fish to get the first salmon?

• 0.2

• 1/0.2

Answer explanation

Tags

CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

Data were collected on the number of days per week that members visit a certain fitness center. The values varied from 0 to 7, and a distribution of relative frequencies for the values was created. Let the random variable X represent the number of days per week that a member visits. The mean of X is 3.12. Which of the following statements is the best interpretation of the mean?

• Each member visits the fitness center 3 or 4 days per week.

• The average number of days that each member visits the fitness center is 3.12 days per week.

• Half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more.

• The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

• For a random sample of members selected from the population, the average number of visits for the sample will be 3.12 days per week.

Answer explanation

Correct. The mean of a random variable is the long-run average based on repeated sampling from the population.

A random sample of size 32 is selected from population X, and a random sample of size 43 is selected from population Y. A 90 percent confidence interval to estimate the difference in means is given as (-1.25, 0.87). Consider a change in the sample sizes such that a random sample of size 52 is selected from population X and a random sample of size 63 is selected from population Y. When all other things remain the same, what effect would such a change have on the interval?

• The width of the interval will increase.

• The width of the interval will decrease.

• The interval will contain no negative numbers.

• The level of confidence will increase.

• The sample means will increase.

Answer explanation

A market research firm is studying the effects of price and type of packaging on sales of a particular product. Twenty-seven stores with shoppers of similar characteristics will be used in the study. The nine combinations of three price levels and three packaging types are the treatments of interest. Total sales of the product over a seven-week period will be recorded. Which of the following describes the best design to use for the study?

• A completely randomized design. Randomly assign the nine combinations of price level and packaging type so that three stores use each combination.

• A completely randomized design. Randomly assign the three price levels so that nine stores use each price level.

• A completely randomized design. Randomly assign the three packaging types so that nine stores use each type of packaging.

• A randomized block design. Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combination.

• A randomized block design. Use packaging as a block. Randomly assign nine stores to each packaging type, then randomly assign price level to the three stores within each block.

Answer explanation

Correct. Because the stores have similar shoppers, a completely randomized design is appropriate. The description of the design, in which the combinations of treatments are randomly assigned to the stores, is correct.

Tags

CCSS.HSS.IC.B.3