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MATH 302 Quiz 3 with Answers

1. The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 24.6 mpg and a standard deviation of 11.2 mpg.  If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 27?
2. A sample of 9 production managers with over 15 years of experience has an average salary of $71,000 and a sample standard deviation of $18,000. Assuming that the salaries of production managers with over 15 years experience are normally distributed, you can be 95% confident that the mean salary for all production managers with at least 15 years of experience is between what two numbers. Place your LOWER limit, rounded to a whole number, in the first blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 54321 would be a legitimate entry. 57164 . Place your UPPER limit, rounded to a whole number, in the second blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 65432 would be a legitimate entry. 84836
3. You are trying to estimate the average amount a family spends on food during a year. In the past, the standard deviation of the amount a family has spent on food during a year has been   $1200. If you want to be 99% sure that you have estimated average family food expenditures within $60, how many families do you need to survey?  Place your answer, a whole number, in the blank 2650 . For example, 1234 would be a legitimate entry.
4. The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 12 employees reveals the following family dental expenses (in dollars): 115, 370, 250, 593, 540, 225, 177, 425, 318, 182, 275, and 228.
5. A lawyer researched the average number of years served by 45 different justices on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the 95% confidence interval estimate for the average number of years served by all Supreme Court justices? Place your limits, rounded to 1 decimal place, in the blanks. Place you lower limit in the first blank. 11.8  Place your upper limit in the second blank.  15.8 When entering your answer do not use any labels or symbols. Simply provide the numerical value. For example, 12.3 would be a legitimate entry.
6. The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 12 employees reveals the following family dental expenses (in dollars): 115, 370, 250, 593, 540, 225, 177, 425, 318, 182, 275, and 228. Construct a 95% confidence interval estimate for the standard deviation of family dental expenses for all employees of this corporation. Place your LOWER limit, in dollars rounded to 1 decimal place, in the first blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 123.4 would be a legitimate entry. 104.7. Place your UPPER limit, in dollars rounded to 1 decimal place, in the second blank. Do not use a dollar sign, a comma, or any other stray mark. For example, 567.8 would be a legitimate entry. 251.3
7. The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives. Determine a 95% confidence interval for the proportion defective for the process today. Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer. 0.044. Place your UPPER limit, rounded to 3 decimal places, in the second blank. For example, 0.345 would be a legitimate entry. 0.131
8. The upper limit of the 90% confidence interval for the population proportion p, given that n = 100; and    = 0.20 is
9. The t- distribution for developing a confidence interval for a mean has _____ degrees of freedom.
10. If you are constructing a confidence interval for a single mean, the confidence interval will___________ with an increase in the sample size.
11. Compute    where t20 has a t-distribution with 20 degrees of freedom.
12. A sample of 23 European countries found that the variance of life expectancy was 7.3 years. What is the 95% confidence interval estimate for the variance of life expectancy in Europe?
13. The average gas mileage of a certain model car is 26 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.3, find the probability that a randomly selected car of this model has a gas mileage between 25.8 and 26.3 miles per gallon.
14. A food snack manufacturer samples 15 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 10.0 and the sample standard deviation is 0.15, find the 95% confidence interval estimate for the true mean.
15. Which of the following will make a confidence interval narrower and more precise?
16. A researcher wishes to know, with 98% confidence, the percentage of women who wear shoes that are too small for their feet. A previous study conducted by the Academy of Orthopedic Surgeons found that 80% of women wear shoes that are too small for their feet. If the researcher wants her estimate to be within 3% of the true proportion, how large a sample is necessary?
17. When you calculate the sample size for a proportion, you use an estimate for the population proportion; namely  . A conservative value for n can be obtained by using     = ______ .
18. A previous study of nickels showed that the standard deviation of the weight of nickels is 150 milligrams. How many nickels does a coin counter manufacturer need to weigh so that she can be 98% confident that her sample mean is within 25 milligrams of the true average weight of a nickel?
19. The lower limit of the 95% confidence interval for the population proportion p, given that n = 300; and    = 0.10 is 0.1339.
20. In developing a confidence interval for the population standard deviation,  , we make use of the fact that the sampling distribution of the sample standard deviation s is not the normal distribution or the t-distribution, but rather a right-skewed distribution called the chi-square distribution, which (for this procedure) has n – 1 degrees of freedom.