Unit 1 Practice

Randomization - A process of randomly assigning subjects to different treatment groups.

• Randomization reduces the impact of confounding variables.

• Randomization is the process of selecting participants for a study

• Randomization is the process of analyzing data from a study

• Randomization is the process of publishing a study

Answer explanation

The question is about the concept of randomization. The correct choice is 'Randomization reduces the impact of confounding variables.' This is because randomization, in a study, is a method used to eliminate bias by distributing confounding variables equally among different treatment groups. This process reduces the impact of these variables on the study results.

A group of researchers are studying the heights of adult men in a large city. They take samples of different sizes from the population. What happens to the mean and standard deviation of their sampling distribution as the size of their samples increases?

• The mean height increases and the standard deviation decreases

• The mean height and standard deviation both increase

• The mean height decreases and the standard deviation increases

• The mean height stays the same and the standard deviation decreases

Answer explanation

As per the central limit theorem, as the sample size increases, the mean of the sampling distribution approaches the population mean, keeping it constant. Meanwhile, the standard deviation decreases as we are averaging over a larger set of data, reducing variability.

Tags

CCSS.6.SP.A.2

What happens to the mean and standard deviation of a sampling distribution as the sample size decreases?

• The mean increases and the standard deviation decreases

• The mean remains same and the standard deviation increases.

• Both the mean and the standard deviation increase

• Both the mean and the standard deviation decrease

Answer explanation

The question asks about the changes in mean and standard deviation in a sampling distribution as the sample size decreases. The correct answer is that the mean remains the same, while the standard deviation increases. This is because the sample size does not affect the population mean, but smaller sample sizes tend to produce larger variations, hence, the increase in standard deviation.

A market researcher collected a data sample by selecting 300 drivers under 35 years of age and 200 drivers over 35 years of age. Identify the sampling technique used by the market researcher.

• Stratified sampling

• Simple random sampling

• Systematic sampling

• Cluster sampling

Answer explanation

The market researcher used 'Stratified sampling' technique. In this method, the population is divided into distinct groups, called strata, and a random sample is drawn from each stratum. Here, the population is divided into groups of 'under 35 years' and 'over 35 years' drivers, hence fitting the definition of stratified sampling.

Tags

CCSS.HSS.IC.B.3

Identify the sampling techniques used and discuss potential sources of bias (if any) After a wildfire, a disaster area is divided into 150 equal grids. Forty grids are selected, and every occupied household in the grid is interviewed to help focus relief efforts on what residents require the most. What type of sampling is used?

• Stratified Sampling

• Cluster Sampling

• Systematic Sampling

• Simple Random Sampling

Answer explanation

The given question describes a situation where a disaster area is divided into equal grids, and a certain number of these grids are selected for interviewing every household within them. This is a characteristic of Cluster Sampling, where the population is divided into separate groups, or clusters, and a random sample of these clusters are selected.

Tags

CCSS.HSS.IC.B.3

1.     In a recent survey, 834 employees in the United States were asked if they thought their jobs were highly stressful. Of the 834 respondents, 517 said yes. Identify population.

• The 834 employees who responded to the survey

• The 517 employees who said their jobs were highly stressful

• All employees in the United States

• The 317 employees who said their jobs were not highly stressful

Answer explanation

The population in a study refers to the entire group that the study applies to. In this question, the study is about the stress levels of employees in the United States. Although the survey was conducted among 834 employees, the findings are intended to represent all employees in the United States. Hence, the correct answer is 'All employees in the United States'.

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CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal, with μ = 17.5 suitcases and σ = 2.9. Let X= the number of suitcases lost. What is the number of suitcases lost with a 43% likely chance in any given week?

• 16 suitcases

• 17 suitcases

• 18 suitcases

• 19 suitcases

Answer explanation

The distribution of the number of suitcases that get lost each week on a certain route is said to be normal with a mean(μ) of 17.5 suitcases and standard deviation(σ) of 2.9. The number of suitcases lost with a 43% likely chance in any given week is 18 suitcases.

Tags

CCSS.HSS.ID.A.4

In a random sample of 75 computers, the mean repair cost was $225. Assume the population standard deviation is $56. If a 99% confidence level were used to construct, an interval for the population means repair cost; what would be the effect on the confidence interval if it was lowered to a 95% confidence level?

• The confidence interval would become wider

• The confidence interval would become narrower

• The confidence interval would remain the same

• The confidence interval would become zero

Answer explanation

The confidence level is inversely related to the width of the confidence interval. When the confidence level increases, the interval becomes wider to accommodate more possibilities. Conversely, when the confidence level decreases, as from 99% to 95%, the interval narrows. Therefore, 'The confidence interval would become narrower' is the correct choice.

What is the effect on the mean and standard deviation of a sampling distribution as the sample size approaches infinity?

• Both the mean and the standard deviation approach infinity.

• The mean remains constant and the standard deviation increases.

• The mean increases and the standard deviation remains constant.

• The mean approaches the population mean and the standard deviation approaches zero.

In a clinical trial, participants are randomly assigned to either a treatment group or a control group. What is the primary purpose of this random assignment?

• To eliminate selection bias and ensure comparability between groups.

• To simplify the data analysis process.

• To ensure that the treatment is effective.

• To increase the sample size of the study.