An online bookseller is considering selling an ereader but w

An online bookseller is considering selling an e-reader but will only do so if they have evidence that the proportion of customers that that will likely purchase one is at least 0.4.Based on a survey of 25customers ,it was found that 8 of them stated that they would likely purchase an e-reader .What should the bookseller do ?

Solution

pcap = 8/25 = .32

Now, Standard deviation can be taken out by the formula = sqrt( p *p\' / n) = sqrt(.25*.75/25) = .0866

So, lets see the t statistic = .32- .40 / (.0866) = -.92

So, a t statistic of -.92 at a df of 25-1=24 means that the difference is not significant.

If the difference is not significant then the bookseller must assume that 8 out of 25 is not significantly different than atleast .4. SO he should go ahead and sell the e-readers.