Below are the data collected from two random samples of 100 members of a large travel club regarding the type of vacation they prefer:
A: 74, 5, 2, 19
B: 71, 6, 2, 21
Which of the following inferences can be made based on the data? (5 points)
A. More members prefer a cruise vacation and a ski vacation than an adventure vacation.
B. More members prefer a beach vacation and a ski vacation than a cruise vacation.
C. Most members prefer a beach vacation.
D. Most members prefer a cruise vacation.
Option B. More members prefer a beach vacation and a ski vacation than a cruise vacation can be inferred from the data, as option A and D cannot be concluded based on the given information. Option C cannot be inferred as none of the options have a majority of the sample size.
To make the inference based on the data provided, we need to compare the preferences for each type of vacation across the two samples.
Here are the preferences for each type of vacation in each sample:
Sample A: 74 members prefer a cruise vacation, 5 prefer a ski vacation, 2 prefer an adventure vacation
Sample B: 71 members prefer a beach vacation, 6 prefer a ski vacation, 2 prefer an adventure vacation
Now let's compare the preferences for each type of vacation:
- For a cruise vacation: Sample A has 74 members, while Sample B has no preference for a cruise vacation. Therefore, we cannot conclude that more members prefer a cruise vacation compared to other vacation types. So, inference A is not valid.
- For a beach vacation: Sample A has no preference for a beach vacation, while Sample B has 71 members preferring a beach vacation. Therefore, we can infer that more members prefer a beach vacation in Sample B. So, inference C is valid.
- For a ski vacation: Sample A has 5 members preferring a ski vacation, while Sample B has 6 members preferring a ski vacation. Therefore, we cannot conclude that more members prefer a ski vacation compared to other vacation types. So, inference B is not valid.
- For an adventure vacation: Both samples have only 2 members preferring an adventure vacation. Therefore, we cannot conclude that more members prefer an adventure vacation compared to other vacation types. So, no inference can be made for this choice.
Based on the data provided, the valid inference is:
C. Most members prefer a beach vacation.