Question

Hoping to attract more shoppers, a city builds a new public parking garage downtown. The city plans to pay for the structure through parking fees. The consultant, who advised the city on this project, randomly selected 44 weekdays. Daily fees collected averaged $126. Based on data from other parking structures, the consultant will assume parking fees at this parking garage are Normally distributed with a standard deviation of $15. If a 95% confidence interval was constructed, how would the margin of error compare to one used to create a 90% confidence interval

Answer 1

`MOE_(95) = 1.192\cdot MOE_(90)`

Explanation:

The margin of error is computed using the formula:

`MOE=z_(\alpha/2)\cdot(\sigma)/(√(n))`

The critical of z for 95% confidence level and 90% confidence level are:

`z_(0.05/2)=z_(0.025)=1.96\\\\z_(0.10/2)=z_(0.05)=1.645`

*Use a z-table.

The sample size is n = 44.

Compare the MOE for 95% confidence level and 90% confidence level as follows:

`(MOE_(95))/(MOE_(90))=(1.96* (15/√(44)))/(1.645* (15/√(44)))`

`(MOE_(95))/(MOE_(90))=(1.96)/(1.645)\\\\(MOE_(95))/(MOE_(90))=1.192\\\\MOE_(95) = 1.192\cdot MOE_(90)`