Question

making an inference in two sample surveys, 125 people were asked about their favorite fruit. in the first survey, 40 people chose apples, 64 chose oranges, and 21 chose bananas. in the second, 43 chose apples, 63 chose oranges, and 19 chose bananas. marianne inferred that most people prefer oranges. is this inference true based on the data? explain.

Explanation:

Step1: Sum total respondents

Total people surveyed = $125 + 125 = 250$

Step2: Sum apple preferences

Total apple votes = $40 + 43 = 83$

Step3: Sum orange preferences

Total orange votes = $64 + 63 = 127$

Step4: Sum banana preferences

Total banana votes = $21 + 19 = 40$

Step5: Compare vote counts

Oranges have the highest total votes, and $\frac{127}{250} = 0.508$, which is over 50% of all responses.

Answer:

Yes, this inference is true. When combining the results of both surveys, oranges received 127 out of 250 total votes, which is the highest number of votes and represents a majority (50.8%) of all respondents. This means oranges are the most preferred fruit in the combined survey data.