Question

# You work on a traffic management team for the city. There has been a proposal to...

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 887. 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 38.

You randomly select 49 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 887, then for 95% of all samples of size n = 49, the sample mean will be somewhere between  and  cars.

b)Over the 49 days, you find that an average of 902 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

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