Question

An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via​ "smart phones," so they want to estimate the proportion of users who access the site that way​ (even if they also use their computers​ sometimes). They draw a random sample of 300300 investors from their customers. Suppose that the true proportion of smart phone users is 4242​%. Complete parts a through c below. ​a) What would you expect the shape of the sampling distribution for the sample proportion to​ be?

Answer 1

The shape of the sampling distribution for the sample proportion is going to be normal with mean
`\mu = 0.42` and
`\sigma = \sqrt{(0.42*0.58)/(300)} = 0.0285`.

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, a large sample size can be approximated to a normal distribution with mean
`\mu` and standard deviation
`(\sigma)/(√(n))`

So the shape of the sampling distribution for the sample proportion is going to be normal with mean
`\mu = 0.42` and
`\sigma = \sqrt{(0.42*0.58)/(300)} = 0.0285`.