The time taken to complete tax return has been a priority in the Tax Return Office in Australia. An officer testing a new website used to fill and launch the tax return took a random sample of 45 taxpayers from the system and found a mean of 156.75 minutes to complete tax return. The time taken is assumed to be Normally distributed with a standard deviation of 18.54 minutes.

The time taken to complete a tax return has been a priority in the Tax Return Office in Australia. An officer testing a new website used to fill and launch the tax return took a random sample of 45 taxpayers from the system and found a mean of 156.75 minutes to complete a tax return. The time taken is assumed to be Normally distributed with a standard deviation of 18.54 minutes. (a)(i). Calculate a 90% confidence interval for the population mean time taken to complete the tax return. Show all steps in your calculation and answer to three decimal places. (ii). Provide an interpretation of the confidence interval calculated in part (i).(b) Later, it was discovered that the standard deviation was 28.1 minutes and not 18.54 minutes. Without any calculation, explain how the new standard deviation would change the confidence interval obtained in part (a). Comment on the accuracy of this condence interval compared to the one in (a) (i)