Below are the data collected from two random samples of 100 members of a large travel club regarding the type of vacation they prefer:
Sample a: 74, 5, 2, 19
Sample 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.
None of the inferences can be made based on the given data.
To make inferences based on the data, let's analyze the preferences for each type of vacation in both sample a and sample b.
Step 1: Calculate the total number of preferences for each vacation type in sample a:
- Cruise vacation: 74 + 5 = 79
- Ski vacation: 2 + 19 = 21
- Adventure vacation: 0
Step 2: Calculate the total number of preferences for each vacation type in sample b:
- Cruise vacation: 71 + 6 = 77
- Ski vacation: 2 + 21 = 23
- Adventure vacation: 0
Step 3: Compare the total number of preferences for each vacation type in both sample a and sample b.
- Cruise vacation: sample a has 79 preferences, sample b has 77 preferences.
- Ski vacation: sample a has 21 preferences, sample b has 23 preferences.
- Adventure vacation: both sample a and sample b have 0 preferences.
Based on this data, we cannot infer the preferences for an adventure vacation since there are no preferences recorded in either sample.
Now, let's analyze the remaining options for inferences.
Option A: More members prefer a cruise vacation and a ski vacation than an adventure vacation.
- This inference is supported because both vacation types (cruise and ski) have more preferences compared to adventure, as calculated in step 3.
Option B: More members prefer a beach vacation and a ski vacation than a cruise vacation.
- We cannot determine the number of preferences for beach vacations since the data only includes preferences for cruise, ski, and adventure vacations.
Option C: Most members prefer a beach vacation.
- We cannot determine if most members prefer a beach vacation since there are no preferences recorded for beach vacations in the data.
Option D: Most members prefer a cruise vacation.
- Since cruise vacation had the highest number of preferences in both sample a (79) and sample b (77), it can be inferred that most members prefer a cruise vacation.
Based on the data, the inference that can be made is:
D. Most members prefer a cruise vacation.