А се College Board AP Classroom Unit 7 Progress Check: MCQ Part C Qichen х (1 of 18 ) Question 1 Two community service groups, J and K, each have less than 100 members. Members of both groups volunteer each month to participate in a community wide recycling day. A study was conducted sa Investigate whether the mean number of days per year of participation was different for the two groups A random sample of 45 members of group Janda random sample of 12 members of group selected. The number of recycling days each selected member participated in for the past 12 months was recorded, and the means for both groups were calculated. A two-sample test for a difference in means will be conducted. Subm Which of the following conditions for inference have been met? L. The data were collected using a random method IL Each sample size is less than 10 percent of the population site III. Each sample size is large enough to assume normality of the sampling distribution of the difference in sample means I only B II only Ill only D I and III only E LII and III Å College Board AP
The Correct Answer and Explanation is :
The correct answer is D. I and III only.
Explanation:
To perform a two-sample test for the difference in means, there are specific conditions that need to be met to ensure valid results. Let’s break down the options based on the conditions:
- Condition I: The data were collected using a random method.
- Met. The problem states that the study involved random samples from both group J (45 members) and group K (12 members), satisfying the condition for random sampling.
- Condition II: Each sample size is less than 10 percent of the population size.
- Not Met. This condition addresses the idea that the sample size should not be too large in comparison to the population, as that could cause issues with the independence of the samples. Although the exact population sizes are not given, it is mentioned that both groups have fewer than 100 members, meaning that each sample size (45 and 12) could be more than 10% of the respective group size. Therefore, this condition is not guaranteed to be met, and we cannot assume it holds based on the information provided.
- Condition III: Each sample size is large enough to assume normality of the sampling distribution of the difference in sample means.
- Met. The sample sizes (45 for group J and 12 for group K) are large enough to assume the sampling distribution of the difference in means will be approximately normal. For smaller sample sizes, it is recommended to check the data for normality using visual methods (such as histograms or Q-Q plots), but based on the given sample sizes, we can reasonably assume the normality condition is satisfied.
Conclusion:
Given that conditions I and III are met, but condition II is uncertain, the correct answer is D. I and III only.