Question

An investment website can tell what devices are used to access their site. The site managers wonder whether they should enhance the facilities for trading via smartphones so they want to estimate the proportion of users who access the site that way. They draw a random sample of 387 investors from their customers. Suppose that the true proportion of smartphone users is 38%. Complete parts​ a. through​ c. below.

a. What would the managers expect the shape of the sampling distribution for the sample proportion to​ be?
b. What would be the mean of this sampling​ distribution?
c. What would be the standard deviation of the sampling​distribution?

Answer 1

Answer:

a) Normal

b) Mean = 0.38

c) Standard deviation = 0.0247

Step-by-step explanation:

a) The shape of the sampling distraction is normal because the sampling distribution depends on the mean and standard deviation.

b) The mean of the sampling distribution will be equal to the true proportion of smart phone users.

The true proportion of smart phone users = 38% = 0.38

p = 0.38

c) Standard deviation α = √ pq/n

p = 0.38

q = 1 - p

q = 1 - 0.38

= 0.62

n = 387

α = √ (0.38*0.62)/387

= √0.2356/387

= √0.0006087855

= 0.0247

The standard deviation = 0.0247