6. In a survey of 2332 adults in a recent year, 1309 say they have made a New Year's resolution. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. 7. A researcher wishes to estimate, with 95% confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within 3% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 40% of the respondents said they eat fast food four to six times per week. (c) Compare the results from parts (a) and (b). 8. In a survey of 3378 adults, 1415 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results. 9. The lengths of lumber a machinecuts are normally distributed with a mean of 106 inches and a standard deviation of 0.4 inch.(a) What is the probability that a randomly selected board cut by the machine has a length greater than 106.15 inches?(b) A sample of 45 boards is randomly selected. What is the probability that their mean length is greater than 106.15 inches? 10. The mean per capita daily water consumption in a village in Bangladesh is about 83 liters per person and the standard deviation is about 1 1.9 liters per person. Random samples of size 50 are drawn from this population and the mean of each sample is determined. a) Find the mean and standard deviation of the sampling distribution of sample means. b) What is the probability that the mean per capita daily water consumption for a given sample is more than 85 liters per person?, c) What is the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person? d) 1 1. A researcher claims that the mean annual cost of raising a child (age two and under) by husband -wife families in rural areas is $ 11,060. In a random sample of husband-wife families in rural areas, the mean annual cost of raising a child (age 2 and under) is $10,920. The sample consists of 800 children. Assume the population standard deviation is $1561. At a = 0.01, is there enough evidence to reject the claim. 12. A consumer group claims that the mean annual consumption of peanut by a person in the United States is greater than 6.5 pounds. A random sample of 60 people in the United States has a mean annual peanut consumption of 6.8 pounds. Assume the population standard deviation is 2.1 pounds. At a = 0.01, can you support the claim
