An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is $250 and the standard deviation of the loss is $1000. The distribution of losses is strongly right-skewed: many policies have $0 loss, but a few have large losses. (1) A random sample of 100 losses was observed, and the mean amount of loss for the sample was calculated. Describe the sampling distribution of the sample mean. A) Approximately normal with mean = $250, standard deviation = $10 B) Approximately normal with mean = $250, standard deviation = $100 C) Skewed right with mean = $250, and standard deviation = $1000 D) Skewed right with mean = $250, and standard deviation = $100 (2) We know this because of: A) The 68 - 95 - 99.7 Rule C) The Central Limit Theorem B) The Pythagorean Theorem D) The Law of Large Numbers (3) What happens to the mean and standard deviation of the distribution of sample means as the size of the sample decreases? A) The mean increases and the standard error stays the same. B) The mean decreases and the standard error increases C) The mean stays the same and the standard error increases. D) The mean stays the same and the standard error decreases. (4) Suppose a population has a mean of 7 for some characteristic of interest and a standard deviation of 9.6. A sample is drawn from this population of size 64. What is the standard error of the mean? A) 0.7 B) 3.3 C) 0.15 D) 1.2(5) From a random sample of workers at a large business, you find that at least 44% of the 169 sampled took a weeklong vacation away from home last year. An approximate 95% confidence interval is 0.38 60 B) Ho: M = 60 and HA: /