Question

A market researcher for a provider of music player accessories wants to know the proportion of customers who own cars to assess the market for a new car charger. A survey of 400400 customers indicates that 7373​% own cars. ​a) What is the estimated standard deviation of the sampling distribution of the​ proportion? ​b) How large would the estimated standard deviation have been if he had surveyed only 100100 customers​ (assuming the proportion is about the​ same)?

Answer 1

a) The estimated standard deviation of the sampling distribution of the​ proportion is 0.023

b) the estimated standard deviation have been if he had surveyed only 100 customers is 0.046

Explanation:

given information:

the number of sample, n = 400

sample proportion, p = 70% = 0.7

a) standard deviation of a sample proportion is

σ =
`\sqrt{(p(1-p))/(n)}`

=
`\sqrt{(0.7 (1-0.7))/(400) }`

= 0.023

b) if n = 100, so

σ =
`\sqrt{(p(1-p))/(n)}`

=
`\sqrt{(0.7 (1-0.7))/(100) }`

= 0.046