Question

An analyst for BC Transit believes that 10% of busses run behind schedule; however, he wishes to confirm his beliefs by constructing an interval estimate for the proportion of all buses that run behind schedule. He desires a 90% level of confidence and is willing to accept no more than a 3 percentage-point margin of error. [Show ALL your work. No marks will be awarded without supporting calculations]

Answer 1

Solution :

Given that,

= 0.10

1 - = 1 - 0.10 = 0.90

margin of error = E = 3% = 0.03

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.645 / 0.03)2 * 0.10 * 0.90

=270.60

Sample size = 271