Question

question 1
1 pts
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

the center of the sampling distribution.

a probability that will be used to summarize evidence against the claim.

the initial assertion about the population parameter.

the sample result that was obtained from the surveyed students.

a standardized value that measures the distance between the sample and population values.

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}$ is calculated as $\hat{p}=\frac{x}{n}$, where $x$ is the number of successes (students living on campus) and $n$ is the sample size.
Here, $x = 48$ and $n=150$. So, $\hat{p}=\frac{48}{150}=0.32$.

Step2: Analyze each option

• Option 1: The center of the sampling distribution is the population proportion $p$. Here $p = 0.29

eq0.32$.

• Option 2: A probability used to summarize evidence against the claim is the $p - value$. $0.32$ is not a probability in this context.
• Option 3: The initial assertion about the population parameter is $p = 0.29

eq0.32$.

• Option 4: Since $\hat{p}=\frac{48}{150}=0.32$, and $\hat{p}$ is the sample result (sample proportion of students living on campus).
• Option 5: A standardized value (z - score) is calculated as $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$. $0.32$ is not a z - score.

Answer:

the sample result that was obtained from the surveyed students.