An investment website can tell what devices are used to access the site. The sit

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 300 investors from their customers. Suppose that the true proportion of smart phone users is 37%. a) What would the standard deviation of the sampling distribution of the proportion of the smart phone users be? b) What is the probability that the sample proportion of smart phone users is greater than 0.37? c) What is the probability that the sample proportion is between 0.31 and 0.43?

Explanation / Answer

a) here p=0.37

n=300

hence std error =(p(1-p)/n)1/2 =0.0279

b) 0.5 as 0.37 lies in middle

c)P(0.31<X<0.43)= P((0.31-0.37)/0.0279<Z<(0.43-0.37)/0.0279)= P(-2.1525 <Z<2.1525)=0.9843-0.0157=0.969

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