1. 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 110 small businesses in the Downtown business district and finds that 18 do not use energy-efficient lights. The committee will choose the Downtown business district as a location that receives educational material about energy-efficient lights if their sample data provide sufficient evidence to support that the true proportion of small businesses that do not use energy-efficient lights is greater than 0.07. A test of hypothesis is conducted.

Part a)What is the null hypothesis? A. The true proportion of small businesses that do not use energy-efficient lights is 0.07. B. The sample proportion of small businesses that do not use energy-efficient lights is greater than 0.07. C. The true proportion of small businesses that do not use energy-efficient lights is lower than 0.07. D. The sample proportion of small businesses that do not use energy-efficient lights is lower than 0.07. E. The true proportion of small businesses that do not use energy-efficient lights is greater than 0.07. F. The sample proportion of small businesses that do not use energy-efficient lights is 0.07.

Part b)What is the alternative hypothesis? A. The true proportion of small businesses that do not use energy-efficient lights is 0.07. B. The sample proportion of small businesses that do not use energy-efficient lights is greater than 0.07. C. The true proportion of small businesses that do not use energy-efficient lights is lower than 0.07. D. The sample proportion of small businesses that do not use energy-efficient lights is lower than 0.07. E. The true proportion of small businesses that do not use energy-efficient lights is greater than 0.07. F. The sample proportion of small businesses that do not use energy-efficient lights is 0.07.

Part c)Assuming that 7% of all Downtown small businesses do not use energy-efficient lights, what model does the sample proportion of small businesses that do not use energy-efficient lights follow? A. N(0.07, 0.25515) B. N(0.07, 0.02433) C. Bin(110, 0.07000) D. N(0.07, 0.00232) E. N(0.07, 2.67600)

Part d)Assuming that 7% of all Downtown small businesses do not use energy-efficient lights, is the observed proportion based on the 110 sampled small businesses unusually low, high, or neither? A. unusually low B. neither C. unusually high

2. At the beginning of an introductory statistics course, students take a test to assess their knowledge in R. Last year, 2000 students took the assessment, and 64% passed. This year, half of the students were randomly selected to attend a one-hour R tutorial before taking the assessment. In a random sample of 100 students who attended the tutorial, 68% passed the test.

Part a)To test if the passing rate has increased from last year for students who attended the tutorial, what will be the null hypothesis? A. The proportion of 1000 students who attended the tutorial and subsequently passed the assessment equals 0.68. B. The proportion of 1000 students who attended the tutorial and subsequently passed the assessment equals 0.64. C. The proportion of 1000 students who attended the tutorial and passed the assessment is higher than 0.64. D. The proportion of 100 students who attended the tutorial and passed the assessment is higher than 0.64. E. The proportion of 100 students who attended the tutorial and subsequently passed the assessment equals 0.64. F. The proportion of 100 students who attended the tutorial and subsequently passed the assessment equals 0.68.

Part b)For the test mentioned in the previous part, what will be the alternative hypothesis? A. The proportion of 1000 students who attended the tutorial and subsequently passed the assessment equals 0.68. B. The proportion of 1000 students who attended the tutorial and subsequently passed the assessment equals 0.64. C. The proportion of 1000 students who attended the tutorial and passed the assessment is higher than 0.64. D. The proportion of 100 students who attended the tutorial and passed the assessment is higher than 0.64. E. The proportion of 100 students who attended the tutorial and subsequently passed the assessment equals 0.64. F. The proportion of 100 students who attended the tutorial and subsequently passed the assessment equals 0.68.

Part c) What is the approximate null model for the sample proportion of the students in the tutorial that passed the assessment