Preparing to Test a Claim about a Population Proportion
Question 6 • AQR_A_IC
A teacher claims that 55% of her statistics students have a strong understanding of inference for one proportion. To investigate this claim she randomly selects 25 of her 50 statistics students and provides them with an inference problem about one proportion. Of the 25 selected students, 14 demonstrate a strong understanding of inference for one proportion. The teacher would like to know if the data provide convincing evidence that more than 55% of her students have a strong understanding of this topic. Are the conditions for inference met?
Answer
A
Yes, the conditions for inference are met.
B
No, the 10% condition is not met.
C
No, the Large Counts Condition is not met.
D
No, the randomness condition is not met.
Explanation
The sample was randomly selected, so the randomness condition is met. For a one-proportion test, the 10% condition requires the sample to be no more than 10% of the population when sampling without replacement; here, 25 of 50 students is 50%. The Large Counts Condition is met under the claim because 25(0.55) = 13.75 and 25(0.45) = 11.25, both at least 10. So the conditions are not all met because the 10% condition fails.
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