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

Answer:

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

Step-by-step 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 $\frac{\sigma}{\sqrt{n}}$

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