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 131 investors from their customers. Suppose that the true proportion of smartphone users is 26 %. 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 samplingdistribution?

a) Unimodal and symmetric (Normal distribution)

b) Mean of the sampling distribution = 0.26

c) Standard deviation of the sampling distribution = 0.0383

Step-by-step explanation:

Sample size, n = 131

Proportion of smart phone users = 26%

p = 26/100 = 0.26

q = 1 - p = 0.74

np = 131 * 0.26 = 34.06

nq = 131 * 0.74 = 96.94

Both the sizes of those that use smart phone and those that do not use are large enough to be modeled by normal distribution.

The shape is therefore unimodal and symmetric

b) What would be the mean of this sampling distribution?

Mean, μ = the proportion of those that use smart phones

μ = 0.26

c) Standard deviation of the sampling distribution

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