Question
A population of interest has a proportion of \( p=0.24 \). Consider a sampling distribution of the sample proportions for 1000 samples of sample size \( n=180 \). You may use the Sampling Distribution tool to answer the following. What value should be in the center of the distribution? 1000 180 0.24 43.2
Ask by Howell Ross. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The center of the distribution is \( 0.24 \).
Solution
In a sampling distribution of sample proportions, the center of the distribution is represented by the population proportion \( p \).
Given that the population proportion \( p = 0.24 \), the value that should be in the center of the distribution is:
\[
\text{Center of the distribution} = p = 0.24
\]
Thus, the correct answer is \( 0.24 \).
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Simplify this solution Bonus Knowledge
In the sampling distribution of sample proportions, the center of the distribution is equal to the population proportion \( p \). Since you provided that the population proportion is \( p = 0.24 \), the center of the distribution for the sample proportions of the samples Of size \( n=180 \) is \( 0.24 \). It's also important to note that, in sampling distributions, most values will cluster around this center, typically forming a normal distribution as the sample size increases. So, 0.24 is your go-to value for the center!
