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 200 investors from their customers. Suppose that the true proportion of smart phone users is 36%.
a) What would you expect the shape of the sampling distribution for the sample proportion to be?
b) What would be the mean of this sampling distribution?
c) If the sample size were increased to 500, would your answers change? Explain.