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 32% of the community support the law. You decide to survey 100 people, and nd that 27% of this survey support the law. a) Based on the assumption that the population proportion is 32%, calculate the zscore of the sample proportion in your survey. Give your answer as a decimal to 2 decimal places. b) Determine the proportion ofthe standard normal distribution that lies to the left of this zscore. That is, determine the area to the left of this zscore in the standard normal distribution. You may nd this standard normal table useful. Give your answer as a percentage to 2 decimal places. Arapwa c) Denote by x% the percentage proportion you calculated in part b). Consider the following ve potential conclusions: A: There is a chance ofx% that your friend is correct, that the true population proportion is 32%. B: If your colleague is conect and the ti'ue population proportion is 32%, then x% of all samples will produce a sample proportion of 27% or lower. C: If your colleague is correct and the true population proportion is 32%, then x% of all samples will produce a sample proportion of 22% or higher. D: There is a chance of x% that the true population proportion is 32% or lower. E: 111ere is a chance of x% that the ti'ue population proportion is 32% or higher. Select the statement that can be inferred from your ndings: You work on a ti'afc 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 865. You intend to tat this hypothesis. For the purposes ofthis 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 ti'afc going through this intersection. a) Complete the following statement by lling in the correct numbers. Give your answers to the nearest whole number of cars. If the toe population mean really is 865, then for I35% of all samples of size n = 42, the sample mean will be somewhere between |:| and |:| cars. b) Over the 42 days, you nd that an average of 879 cars pass through the intersection. Therefore with 95% condence you O can rule out the possibility that your colleague's hypothesis was correct 0 cannot rule out the possibility that your colleague's hypothesis was correct