Question

A market survey was conducted to determine whether a company's new product suits the preference of the public. Out of 400 people, the surveyresults showed that 320 liked the new product.What is the mean and standard deviation of the sample proportion?

Answer 1

• Mean = 0.8

,

• Standard Deviation = 0.02

Explanation:

(a) Mean

Out of 400 people, the survey results showed that 320 liked the new product.

`\begin{gathered} Mean,p=(320)/(400) \\ p=0.8 \end{gathered}`

The mean of the sample proportion is 0.8.

(b)Standard Deviation

The standard deviation of the sample proportion is calculated using the formula:

`\begin{gathered} \sigma_p=\sqrt{(p\left(1-p\right))/(n)} \\ =\sqrt{(0.8\left(1-0.8\right))/(400)} \\ =\sqrt{(0.8*0.2)/(400)} \\ =0.02 \end{gathered}`

The standard deviation of the sample proportion is 0.02.