Question

1. a compact disc (cd) manufacturer wanted to determine which of two different cover designs for a newly released cd will generate more sales. the manufacturer chose 70 stores to sell the cd. thirty - five of these stores were randomly assigned to sell cds with one of the cover designs and the other 35 were assigned to sell the cds with the other cover design. the manufacturer recorded the number of cds sold at each of the stores and found a significant difference between the mean number of cds sold for the two cover designs. which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion? (a) it is not reasonable to conclude that the difference in sales was caused by the different cover designs because this was not an experiment. (b) it is not reasonable to conclude that the difference in sales was caused by the different cover designs because there was no control group for comparison. (c) it is not reasonable to conclude that the difference in sales was caused by the different cover designs because the 70 stores were not randomly chosen. (d) it is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores. (e) it is reasonable to conclude that the difference in sales was caused by the different cover designs because the sample size was large. 2. researchers conducted a study to investigate whether watching an outdoor scene while exercising improves more than exercise alone. fourteen fifth - grade students participated in two trials of the study. for one trial, students rode a stationary bicycle for 15 minutes while watching a video of someone cycling through a for the other trial, the students rode a stationary bicycle for 15 minutes without watching a video. each studen completed both trials in a randomized order. the researchers recorded the students heart rates after each tr. 3. under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling? (a) the population can be divided into a large number of strata so that each stratum contains only a few individuals. (b) the population can be divided into a small number of strata so that each stratum contains a large number of individuals. (c) the population can be divided into strata so that the individuals in each stratum are as much alike as possible. (d) the population can be divided into strata so that the individuals in each stratum are as different as possible. (e) the population can be divided into strata of equal sizes so that each individual in the population still has the chance of being selected.

Explanation:

Question 1

This is an experiment where the cover designs (the treatment) were randomly assigned to stores. Random assignment helps to ensure that other variables that could affect sales are evenly distributed between the two groups (the two cover - design groups). So, we can attribute the difference in sales (if any) to the cover designs.

• Option (A) is wrong because it is an experiment (treatments - cover designs - are assigned).
• Option (B) is wrong because there is no need for a traditional control group (a group with no treatment) when we are comparing two active treatments (two cover designs).
• Option (C) is wrong because the stores were randomly assigned to the cover designs (the problem states "randomly assigned").
• Option (E) is wrong because sample size alone does not make a causal conclusion valid; random assignment does.

In a randomized matched - pairs experiment, each subject (in this case, each student) serves as their own control. Here, each of the 14 students participates in both trials (with and without watching the outdoor scene video). The order is randomized to control for order effects.

• Option (B) is wrong because there is no placebo (a fake treatment) in this study.
• Option (C) is wrong because in a completely randomized experiment, subjects are randomly assigned to different treatment groups, and here it is the same subjects in both "groups" (trials).
• Option (D) is wrong because it is not a survey (which is about collecting data through questions, not an intervention like exercise with/without video).
• Option (E) is wrong because it is an experiment (there is an intervention - watching the video or not while exercising), not just an observational study (where no treatment is imposed).

Stratified random sampling is preferred over simple random sampling when the population can be divided into strata (sub - groups) where the individuals within each stratum are as much alike as possible. This reduces the variability within each stratum, and when we take samples from each stratum, the overall estimate (e.g., of a population mean) has less variance.

• Option (A) is wrong because having a large number of strata with few individuals is not the ideal situation for stratified sampling (it can be inefficient).
• Option (B) is wrong because the number of strata (small or large) is not the key factor; the homogeneity within strata is.
• Option (D) is wrong because if the individuals in each stratum are different, stratified sampling does not provide the variance - reducing benefit.
• Option (E) is wrong because equal - sized strata are not a requirement for stratified sampling (and it is about homogeneity within strata, not equal size).

Answer:

D. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores.

Question 2