Which of these is not an advantage of using a stratified sample instead of a simple random sample? A) the stratified random sample allows you to get information about each stratum
B) the stratified sample reduces bias
C) the stratified sample reduces sample to sample variability
D) the stratified sample allows you to get more reliable estimates using the same sample size
E) the stratified sample eliminates the need for randomization
_ 2. The principal of a small elementary school wants to select a simple random sample of 24 students. The school has 12 classrooms with 18 students in each class. She decides to randomly select two students from each classroom. Is this a simple random sample?
A) No, because not all combinations of 24 students could have been chosen.
B) No, because each student did not have an equal chance of being selected.
C) Yes, because a stratified sample is a type of simple random sample.
D) Yes, because the students were selected at random.
E) Yes, because each student had an equal chance to be selected.
_ 3. Which is true about randomized experiments?
I. Randomization reduces the effects of confounding variables.
II. Random assignment of treatments allows results to be generalized to the larger population.
III. Blocking can be used to reduce the within-treatment variability.
A) I only B) II only C) III only D) I and III E) all three
_ 4. A school district administrator sent a survey to all teachers in the district. Only 30% of the teachers responded to the survey. Which of the following is true?
I. The people that did not responded are likely to be similar to those that did so he should use them as the sample.
II. This survey design suffered from non-response bias.
III. Because he sent the survey to everyone, this is a census and the results can be applied to the whole population.
A) I only B) II only C) I and II only D) II and III only E) I, II, and III
_ 5. Does Procellera® Antimicrobial Wound Dressing help injuries heal faster? Researchers checked records of 38 patients who had been treated for acute or chronic wounds between 2010 and 2012. They found that those who had been treated with Procellera® healed almost twice as fast. This is a
A) survey B) retrospective study C) prospective study
D) randomized experiment E) matched experiment
_ 6. A company has tried to improve the effectiveness of its dishwashing detergent and wants to see if it works better than the original formula. They use 6 identical new dishwashers and load them identically with dirty dishes. Three packs of each of the two types of detergent are used, and they are randomly assigned to one of the six dishwashers. After the load is run, they rate each load for overall cleanliness. Which of the following is true?
A) The explanatory variable is the different dishwashers. B) The response variable is the type of detergent.
C) Because each brand is used in three dishwashers, replication is used properly.
D) A control group with no detergent at all is needed.
E) Blinding is impossible in this experiment because they must be able to see the dishes.
_ 7. In an experiment the primary purpose of blocking is to
A) reduce the within-treatment variation. B) reduce the between-treatment variation.
C) reduce bias. D) eliminate confounding variables.
E) eliminate the need for random assignment of treatments.
_ 8. A Columbia University study linked soda consumption to behavior problems in children. Researchers examined data from a previous study that followed 2929 mother-child pairs. One survey asked about behaviors of the child and also about soda consumption. They found that the more soda the kids drank, the more behavior problems they had. What aspect of a well-designed experiment is absent from this study?
A) a placebo B) blinding C) randomization
D) a control group E) all of these
_ 9. It was discovered that a larger proportion of children who slept with nightlights later developed nearsightedness, compared to children who did not sleep with nightlights. The headlines read, “Leaving a light on for your children causes nearsightedness” Later it was pointed out that nearsighted people have more trouble seeing in the dark and are more likely to leave lights on at night for their kids. And those same nearsighted parents are likely to have nearsighted kids. This is an example of
A) a lurking variable. B) bias. C) a control group.
D) a placebo E) a randomized block design.
_ 10. In order to see which variety of apple tree produces more fruit, a farmer sets up an experiment. He has three plots of land with different soil and natural water availability. Each plot has room for eight trees. The farmer randomly selects four locations in each plot for the first variety of tree and the other four get the second variety. This experiment is…
A) completely randomized with one factor: the plot of land
B) completely randomized with one factor: the variety of tree
C) randomized block, blocked by plot of land
D) randomized block, blocked by variety of tree
E) completely randomized with two factors
The Correct Answer and Explanation is :
Question 1:
Answer: E) the stratified sample eliminates the need for randomization
Explanation: Stratified sampling involves dividing the population into distinct subgroups (strata) and then taking a random sample from each stratum. It does not eliminate the need for randomization; in fact, randomization is key to ensuring the sample is representative and unbiased. The other options (A, B, C, D) highlight benefits of stratified sampling, such as reduced bias, more reliable estimates, and better representation of different strata.
Question 2:
Answer: A) No, because not all combinations of 24 students could have been chosen.
Explanation: In simple random sampling, every individual in the population should have an equal chance of being selected. In this case, the principal selects two students from each of the 12 classrooms, which means the sample is not truly random because the selection of students is constrained by classroom, and not every possible combination of 24 students could be chosen. This is closer to a stratified sampling design.
Question 3:
Answer: D) I and III
Explanation:
- I. Randomization reduces the effects of confounding variables. This is true because randomization helps eliminate bias from variables that are not controlled for.
- II. Random assignment of treatments allows results to be generalized to the larger population. This is not necessarily true because randomization does not guarantee that the results can be generalized; the sample needs to be representative of the population.
- III. Blocking can be used to reduce the within-treatment variability. This is true because blocking groups similar experimental units together to control for known sources of variation.
Question 4:
Answer: B) II only
Explanation:
- I. The people who did not respond are not likely to be similar to those who did, as non-respondents may have different characteristics.
- II. This survey design suffers from non-response bias because the group that did not respond may have different opinions or characteristics, thus skewing the results.
- III. The survey is not a census because not all individuals participated, so the results cannot be generalized to the entire population.
Question 5:
Answer: B) retrospective study
Explanation: In this case, the researchers are looking at records of patients who were treated in the past, which makes this a retrospective study. In contrast, a prospective study would involve following participants into the future.
Question 6:
Answer: C) Because each brand is used in three dishwashers, replication is used properly.
Explanation: Replication involves using multiple units for each treatment to reduce the variability in the results. By using three dishwashers for each detergent type, the company is properly replicating the treatments. This helps ensure that the results are not due to random chance or a specific dishwasher.
Question 7:
Answer: A) reduce the within-treatment variation.
Explanation: Blocking is used in experimental design to group similar experimental units together. By controlling for certain variables (such as age or gender), blocking helps to reduce variability within the treatment groups, making it easier to detect the effect of the treatments.
Question 8:
Answer: C) randomization
Explanation: The study described is observational, not an experiment, because it does not involve randomization of the participants. Randomization is key to experimental design and would be needed to establish a causal relationship between soda consumption and behavior problems.
Question 9:
Answer: A) a lurking variable.
Explanation: A lurking variable is an unobserved variable that influences both the dependent and independent variables, potentially causing a spurious association. In this case, nearsightedness may be a lurking variable that influences both the tendency to sleep with a nightlight and the likelihood of developing nearsightedness, explaining the observed correlation.
Question 10:
Answer: C) randomized block, blocked by plot of land
Explanation: In this experiment, the farmer blocks by plot of land, with each plot receiving two types of trees (the two treatments). Within each block (plot of land), the trees are randomly assigned to the two varieties. This ensures that the effect of the soil and water conditions is controlled for, making it a randomized block design.