Question

1. The Luxor Computer Company plans to introduce a pyramid-shape computer. The

company is interested in the proportion of customers who find the unusual shape a positive selling point. In a random sample of 350 potential customers, 203 of the respondents indicated that the shape was a positive selling point.

a. What is an estimate of the proportion of customers who find the unusual shape a positive selling point?

b.What is a 90-percent confidence interval for the proportion of prospective customers who find the unusual shape a positive selling point?

c. How many prospective customers would have to be queried for Luxor to be 90-percent certain that its estimated proportion was within 5% of the true value?

Answer 1

Required proportion p = 203/350=0.58

SD = [ p*(1-p)/n]^05 = [0.58*0.42/350]^0.5 =0.02638

Confidence interval = mean +- z*SD

z for 90% confidence interval is 1.96

Interval for proportion

= 0.58+-0.02638*1.96 =0.58+- 0.0517

= 0.6317 to 0.5283

c. Number of customers needed = (z)^2 * p*(1-p) / (e)^2

= 1.96x1.96 x 0.58 x0.42 / ( 0.05)x(0.05)

=374.32 =375 customers