Question

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 to 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 J and a random sample of 32 members of group K were 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 t-test for a difference in means will be conducted. Which of the following conditions for inference have been met?I. The data were collected using a random method.II. Each sample size is less than 10 percent of the population size.III. Each sample size is large enough to assume normality of the sampling distribution of the difference in sample means.
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

Answer 1

Answer: III only.

Step-by-step explanation: Those answer choices state that each sample size is less than 10%, and that each sample size is large enough to assume normality of distribution, the data was collected using a random method. The only reasonable choice would be III because it was not used with a random method, isn;t 10% of sample size, so It must be each sample size is large enough to assume normality of the sampling distribution. You can do this by using the process of elimination.

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