1. A random sample of seven 2009 sports cars is taken and their \"in the city\" miles per gallon is recorded. The results are as follows: 20 19 20 19 16 18 22 Assuming the population distribution is normal, calculate a 95% confidence interval for , the population mean \"in the city\" mpg for 2009 sports cars. 2. A random sample of size 12 is drawn from a normal population. The sample standard deviation is s = 3.49. Construct a 95% confidence interval for the population standard deviation . 3. A sample of 20 adult female rats is drawn at random from a large number of rats in an animal house. Among other measurements the uterine weight (in milligrams) is recorded at postmortem for each rat. The sample yields a mean uterine weight of 21mg. Assume = 1.6 mg and normally distributed population. Using the critical value, test whether the population mean uterine weight is less than 21.5 mg, using a level of significance = 0.10. 4. The average life expectancy of an American pit bull terrier is 12 years. Random samples of ages of 12 deceased pit bull terriers are given below. Assume the population is normally distributed. We are interested in whether the population mean life expectancy of the pit bull terrier is less than 12 years, using = 0.10. 10.5 11 9.5 11.5 12.3 12 12.2 13 12.6 12.9 9.8 10.7 5. Suppose a random sample of 15 days in December showed a sample mean of 45.7F. Assume that = 3 and a normally distributed population. Test whether the population mean temperature is less than 49F, using level of significance = 0.05. 6. Population mean length of gray whales in 42 feet. A random sample of 14 adult humpback whales had an average length of 42.5 feet with a standard deviation of 4 feet. Test a level of significance of = 0.01 if the population mean length of humpback whales is different than that of gray whales. 7. A research study measured the pulse rates of 57 college men and found a mean pulse rate of 70.4211 beats per minute with a standard deviation of 9.9480 beats per minute. Researchers want to know if the mean pulse rate for all college men is different from the current standard of 72 beats per minute. Use = 0.05. 8. In the population of Americans who drink coffee, the average daily consumption is 3 cups per day. A university wants to know if their students tend to drink more coffee than the national average. They ask a random sample of 20 students how many cups of coffee they drink each day and found that the sample mean is3.8. Do they have evidence that their students drink more than the national average? Assume that the population standard deviation is 1.5 cups. Use = 0.01. 9. Suppose we would like to determine if the typical amount spent per customer for dinner at a new restaurant in town. A sample of 49 customers over a three-week period was randomly selected and the average amount spent was $22.60. Assume that the population standard deviation is known to be $2.50. Construct a 99% confidence interval for the mean amount spent per customer at this restaurant. 10. To hunt flying insects, bats emit high-frequency sounds and then listen for their echoes. One intersing question is: how far apart are the bat and the insect when the bat first senses that the insect is there. The following data sets gives bat to insect detection distance (in cm) for a random sample of 11 bats. Assuming that the bat to insect detection distance is normally distributed. 62, 52, 68, 23, 34, 45, 27, 42, 83, 56, 40 Test whether the the true bat to in sect detection distance is greater than 50. Use = 0.10