Nirva Derose Instructions: Please work a problem to the best of your ability. Show all work; partial credit will not be awarded if I cannot easily follow and understand your work. Select the best answer for the multiple choice questions. Questions/problems are worth 0.5 point each. 1. The life expectancy in the United States is 75 with a standard deviation of 7 years. A random sample of 49 individuals is selected a. What is the probability that the sample mean will be larger than 77 years? b. What is the probability that the sample mean will be less than 72.7 years? c. What is the probability that the sample mean will be between 73.5 and 76 years? d. What is the probability that the sample mean will be between 73.5 and 76 years? e. What is the probability that the sample mean will be larger than 73.46 years? 2. The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the mean? b. . What is the random variable in this problem? Define it in words c. What is the probability that the average life in the sample will be between 2,670.56 and 2,809.76 hours? d. What is the probability that the average life in the sample will be greater than 3,219.24 hours? e. What is the probability that the average life in the sample will be less than 3,180.96 hours? 3. The makers of a soft drink want to identify the average age of its consumers. A sample of 16 consumers is taken. The average age in the sample was 22.5 years with a standard deviation of 5 years. Assume the population of consumer ages is normally distributed. a. b. c. d. Construct a 95% confidence interval for the average age of all the consumers. Construct an 80% confidence interval for the average age of all the consumers. Construct an 80% confidence interval for the average age of all the consumers. Discuss why the 95% and 80% confidence intervals are different. 4. The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is a. b. c. d. H0: < 40,000 Ha: 40,000 H0: 40,000 Ha: > 40,000 H0: > 40,000 Ha: 40,000 H0: 40,000 Ha: < 40,000 5. The sponsors of televisions shows targeted at the market of 5 - 8 year olds want to test the hypothesis that children watch television at most 20 hours per week. The population of viewing hours per week is known to be normally distributed with a standard deviation of 6 hours. A market research firm conducted a random sample of 30 children in this age group. The resulting data follows: 19.5 29.7 17.5 10.4 19.4 18.4 14.6 10.1 12.5 18.2 19.1 30.9 22.2 19.8 11.8 19.0 27.7 25.3 27.4 26.5 16.1 21.7 20.6 32.9 27.0 15.6 17.1 19.2 20.1 17.7 At a .10 level of significance, use Excel to test the sponsors' hypothesis