An environmental group in a province is considering which business districts need to receive educational material about energy-efficient lights. A committee will decide where these business districts will be located based on the percentage of small businesses that are not using energy-efficient lights. The environmental group takes a simple random sample of 142 small businesses in the Downtown business district and finds that 24 do not use energy-efficient lights. Part 1 a. The proportion ot the 142 small businesses in Downtown business district that do not use energy-efficient lights, %, is a Q A. statistic O B. parameter Q 0. variable of interest b. Use the sample data to compute a 95% confidence interval for the true proportion of small businesses in the Downtown business district that do not use energy-efficient lights. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). 95% confidence interval =( V Part 2 For each of the following statements, specify whether the statement is a correct interpretation of the 95% confidence interval for the true proportion of small businesses in the Downtown business district that do not use energy-efficient lights. a. If many random samples of 142 Downtown small businesses are drawn, 95% of the resulting confidence intervals will contain the value of the true proportion of Downtown small businesses that do not use energy-efficient lights. ? v b. 16.9 % (%) of Downtown small businesses do not use energyefficient light. ? v c. There is a 95% probability that the true proportion of Downtown small businesses that do not use energy-efficient lights equals %. ? v d. If many random samples of 142 Downtown small businesses are drawn, 95% of the resulting confidence intervals will contain the value %. '_) v e. If another random sample of 142 Downtown small businesses is drawn, there is a 95% probability that the sample proportion of Downtown small businesses that do not use energy-efficient lights equals %. ? v Part 3 Suppose that the committee wants to re-estimate the population proportion and wishes for their 95% confidence interval to have a margin of error no larger than 0.01. Assuming this sample proportion stays constant, what's the minimum sample size to achieve this? Please carry answers to at least six decimal places in intermediate steps. I It! A hybrid car is advertised to have a city milage of 38 mpg (miles per gallon). After sufficient test drives, a consumer critic concludes that the mileage is a normal random variable with a mean of 37 mpg and a standard deviation of 5 mpg in their city. Suppose that you draw a random sample of 32 such hybrid cars. Part 3) Using the information about the distribution of the mileage given by the consumer critic, find the probability that the mean mileage of the sample is greater than 38.01 mpg. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion): 0,127 ( Part b) Using the normal approximation, what is the probability that more than 45% of the sampled hybrid cars operate at the advertised mileage (i.e., the mileage exceeds 38 mpg)? (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion)