Question 1:

You work for a lobby group that is trying to convince the government to pass a new law. Before embarking on this, your lobby group would like to know as much as possible about the level of community support for the new law.

Your colleague, based on his research into community opinion on related matters, proposes that 31% of the community support the law. You decide to survey 100 people, and find that 24% of this survey support the law.

a)Based on the assumption that the population proportion is 31%, calculate the z-score of the sample proportion in your survey. Give your answer as a decimal to 2 decimal places.

z =

b)Determine the proportion of the standard normal distribution that lies to the left of this z-score. That is, determine the area to the left of this z-score in the standard normal distribution. You may find thisstandard normal tableuseful. Give your answer as apercentageto 2 decimal places.

Area =%

c)Denote by x% the percentage proportion you calculated in part b). Consider the following five potential conclusions:

A:There is a chance of x% that your friend is correct, that the true population proportion is 31%.

B:If your colleague is correct and the true population proportion is 31%, then x% of all samples will produce a sample proportion of 24% or lower.

C:If your colleague is correct and the true population proportion is 31%, then x% of all samples will produce a sample proportion of 24% or higher.

D:There is a chance of x% that the true population proportion is 31% or lower.

E:There is a chance of x% that the true population proportion is 31% or higher.

Select the statement that can be inferred from your findings:

Question 2.

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 868. 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 42 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 868, then for 90% of all samples of sizen = 42, the sample mean will be somewhere between____and____cars.

b)Over the 42 days, you find that an average of 881 cars pass through the intersection. Therefore with 90% 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