Question

at a large university, it is reported that 46% of all students bring a reusable water bottle to campus each day. if we take many random samples of size ( n = 900 ) from this population, we know the sample proportion who bring a reusable water bottle to campus each day will vary from sample to sample. what will the standard deviation of this sampling distribution be equal to? choose the answer below that is closest to what you calculate. 0.0109 0.0166 0.0125 0.0460 0.0013

Explanation:

Step1: Identify the formula for the standard deviation of a sampling distribution of a proportion

The formula is \(\sigma_{\hat{p}}=\sqrt{\frac{p(1 - p)}{n}}\), where \(p\) is the population proportion and \(n\) is the sample size.

Step2: Substitute the given values into the formula

Given \(p = 0.46\) and \(n=900\). First, calculate \(1-p=1 - 0.46=0.54\). Then \(\frac{p(1 - p)}{n}=\frac{0.46\times0.54}{900}\).

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Step3: Calculate the square - root

\(\sigma_{\hat{p}}=\sqrt{0.000276}\approx0.0166\)

Answer:

0.0166