You work on a traffic management team for the city. There has been a proposal to add a new lane to a road near a busy intersection. As part of the research into whether or not to build the new lane, the team would like to know how many cars, on average, pass through this intersection at peak hour each day (5 pm to 6 pm). Your colleague has developed the hypothesis that the population mean is 870. You intend to test this hypothesis. For the purposes of this research, the team is assuming that the standard deviation in the number of cars passing through each hour is 36.

You randomly select 46 days on which to monitor the traffic going through this intersection.

a)Complete the following statement by filling in the correct numbers. Give your answers to the nearest whole number of cars.

If the true population mean really is 870, then for 95% of all samples of sizen = 46, the sample mean will be somewhere betweenandcars.

b)Over the 46 days, you find that an average of 884 cars pass through the intersection. Therefore with 95% confidence you

can rule out the possibility that your colleague's hypothesis was correct cannot rule out the possibility that your colleague's hypothesis was correct