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AP Statistics 1.11 Random Sampling- Exam Style Questions - MCQs - New Syllabus

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Question

A factory producing smart phones has been criticized for recent quality control issues. A newly hired Quality Control Engineer decides to randomly select one of the first 50 phones to come off the assembly line on a given day. That phone, and every subsequent 50th phone, will be taken off the line, turned on, and checked for quality and reliability. What sampling technique is the Quality Control Engineer employing?

(A) Cluster Sample
(B) Convenience Sample
(C) Simple Random Sample
(D) Stratified Random Sample
(E) Systematic Sample

▶️ Answer/Explanation

In a systematic sample, researchers randomly choose a starting point and then select every kth individual thereafter.

In this problem, the engineer:

• Randomly selects one of the first 50 phones.
• Then inspects every subsequent 50th phone.

This follows the standard procedure for systematic sampling, where:

\(\text{Starting Point} \rightarrow \text{Every } 50^{th} \text{ item}\)

The process is not a simple random sample because not every possible group of phones has an equal chance of being selected. It is also not stratified or cluster sampling because the phones are not divided into groups before sampling.

Therefore, the sampling method used is a systematic sample.

✅ Answer: (E)

Question 

A manufacturing company conducts a study to compare two methods for transporting and storing methyl methacrylate to determine which method results in fewer safety concerns. Method A uses a hydroquinone-based inhibitor and Method B uses a much less common phenothiazine-based inhibitor. The researchers randomly select 20 containers of methyl methacrylate from the containers produced in a day and then randomly assign Method A to 10 of the containers and Method B to the remaining 10 containers. The researchers find that Method A has significantly fewer safety concerns than Method B.

Based on the results of the study, can the researchers state that the decrease in safety concerns is caused by the use of Method A?

(A) Yes, since the methods were randomly assigned to containers.
(B) Yes, since the containers were randomly selected from all containers.
(C) No, the methods needed to be assigned to at least 30 containers.
(D) No, since the researchers should not have both randomly selected containers and randomly assigned the methods to the containers.
(E) No, since the day for selecting the containers was not selected at random.

▶️ Answer/Explanation

The key feature of this study is that the researchers randomly assigned the two treatment methods to the containers. Random assignment allows researchers to control for lurking variables and establish a cause-and-effect relationship between the treatment and the response.

Random sampling helps with generalizing results to a larger population, while random assignment is what justifies causal conclusions. Since Method A and Method B were randomly assigned to the containers, the observed difference in safety concerns can reasonably be attributed to the treatment method.

Therefore, the researchers can conclude that the reduction in safety concerns was caused by Method A.

✅ Answer: (A)

Question 

A pharmaceutical company conducted a clinical trial to evaluate the effectiveness of a new medication for reducing blood pressure. The trial involved 500 volunteers from various age groups and backgrounds. The researchers found a statistically significant reduction in blood pressure among the participants who received the medication. What is a potential concern regarding the scope of inference for this study?

(A) The study did not have a random sample, affecting the ability to generalize.
(B) The standard error will be too large because the sample size is large.
(C) The sample size is too large, leading to statistical outliers.
(D) The study only included participants with high blood pressure.
(E) The study did not control for smoking.

▶️ Answer/Explanation

The study used volunteers, not a random sample from the population. While an experiment with random assignment can support cause-and-effect conclusions, using volunteers may limit the ability to generalize the results to all individuals who might use the medication.

This is a classic scope of inference issue. Without a random sample, the sample may not be representative of the broader population, even if the treatment effect is statistically significant.

The other choices either describe issues not mentioned in the study or make incorrect statements about large sample sizes and standard errors.

✅ Answer: (A)

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