An investment website can determine what devices are used to access the site. The site managers are considering improving the trading facilities for "smart phones" and want to estimate the proportion of users who access the site through this method, even if they also use their computers occasionally. They randomly select a sample of 100 investors from their customer base. Assuming that the true proportion of smart phone users is 44%, complete parts a through c below.
a) What would you expect the shape of the sampling distribution for the sample proportion to be?
A. Exponential
B. Normal
C. Uniform
D. None of these
b) What would be the mean of this sampling distribution?
A. The mean would be ______?
(Type an integer or a decimal.)
B. The mean cannot be determined.
c) If the sample size were increased to 400, would your answers change? Explain.
A. Yes, although the shape and symmetry characteristics would remain, the mean would increase.
B. No, the shape and symmetry characteristics would still be approximately the same and the mean would still be the same.
C. No, the shape, symmetry characteristics, and mean will only change if the sample size is increased by at least 1000.
D. Yes, although the mean would still be the same, the shape and symmetry characteristics would change.