Question

1. university housing officials report that 29% of all college students live on campus. when a researcher surveys a random sample of 150 college students, she finds that 48 of these students live on campus. if the researcher uses this data to conduct a hypothesis test, the number 0.32 represents

a. the center of the sampling distribution.
b. a probability that will be used to summarize evidence against the claim.
c. the initial assertion about the population parameter.
d. the sample result that was obtained from the surveyed students.
e. a standardized value that measures the distance between the sample and population values.

Explanation:

• The population proportion \(p = 0.29\) (given that 29% of all college students live on campus).
• The sample proportion \(\hat{p}=\frac{48}{150}=0.32\). In hypothesis testing for proportions, the sample proportion is the result obtained from the sample data.
• Option A: The center of the sampling distribution for proportions is the population proportion \(p\), not \(\hat{p}\).
• Option B: A probability used to summarize evidence against the claim is the \(p -\)value, not the sample proportion.
• Option C: The initial assertion about the population parameter is the null hypothesis value (here \(p = 0.29\)), not \(\hat{p}\).
• Option E: A standardized value is the \(z -\)score (\(z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}\)), not the sample proportion.

Answer:

D. the sample result that was obtained from the surveyed students.