Question

Problem 5 (7 marks)

A survey of 36 retail stores revealed that the average price of a tablet was $375 with a standard deviation of $20. a) What is the 95% confidence interval to estimate the true cost of the tablet? (4 marks) b) What sample size would be needed to estimate the true average price of a tablet with an error of 5$ ± and a 99% confidence? (3 marks)

Answer 1

Solution :

Given that,

a) Z$\alpha$/2 = Z_0.025 = 1.96

Margin of error = E = Z$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

= 1.96 * ( 20 /  $\sqrt$36 )

= 6.53

At 95% confidence interval estimate of the population mean is,

  ± E

T

= 375  ± 6.53

= ( $368.47, $381.53 )

b) Z_$\alpha$/2 = Z_0.005 = 2.576

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [ 2.576 * 20 / 5 ]²

n = 106.17

Sample size = n = 107