Question 5 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
The manager of a large grocery store wants to inspect an incoming shipment of oranges to determine the proportion of blemishes. One inspector, Mary, takes a random sample of 25 oranges, and another inspector, Pat, takes a random sample of 50 oranges. Which of the following statements about variability of the sample proportion is correct?
Answer
A
The variability of the proportion of blemishes for Mary’s sample will be less than the variability of Pat’s.
B
The variability of the proportion of blemishes for Mary’s sample will be greater than the variability of Pat’s.
C
The variability of the proportion of blemishes for Mary’s sample will be the same as the variability of Pat’s.
D
Since the two inspectors took two different samples, there is no way to compare the variability of the two samples.
Explanation
For a sample proportion, variability decreases as the sample size increases. Pat’s sample of 50 oranges is larger than Mary’s sample of 25, so Pat’s sample proportion is expected to vary less. Therefore, the variability for Mary’s sample will be greater than Pat’s.
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