Question

80 out of 150 people preferred a particular pc. the null hypothesis = 0.40. using a 95% confidence; what is the standard error?
0.033
0.041
0.045
0.035

Explanation:

Step1: Identify the formula for standard error of proportion

The formula for the standard error of a proportion is $SE = \sqrt{\frac{p(1 - p)}{n}}$, where $p$ is the proportion under the null - hypothesis and $n$ is the sample size.

Step2: Determine the values of $p$ and $n$

We are given that the null hypothesis proportion $p = 0.40$ and the sample size $n=150$.

Step3: Calculate the standard error

Substitute $p = 0.40$ and $n = 150$ into the formula:

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However, if we consider the sample proportion $\hat{p}=\frac{80}{150}\approx0.533$ and use the formula $SE=\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$, we have:

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Answer:

B. 0.041