Math 14, Homework 7.1 p. 379 # 7, 9, 18, 20, 21, 23, 25, 26 Name

Transcription

1 7.1 p. 379 # 7, 9, 18, 0, 1, 3, 5, 6 Name 7. Find each. (a) z α Step 1 Step Shade the desired percent under the mean statistics calculator to 99% confidence interval µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ (b) z α 98% confidence interval (c) z α µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ 95% confidence interval µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ (d) z α 90% confidence interval µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ (e) z α 94% confidence interval µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ

2 7.1 p. 379 # 7, 9, 18, 0, 1, 3, 5, 6 9. Fuel Efficiency of Cars and Trucks Since 1975 the average fuel efficiency of U. S. cars and light trucks (SUVs) has increased from 13.5 to 5.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean mileage of 8.1 mpg per vehicle. The population standard deviation is 4.7 mpg per vehicle. The population standard deviation is 4.7 mpg. Estimate the true mean gas mileage with 95% confidence. Step 1 Step Step 3 Find the confidence interval such that P( X z α < µ < X + z α 0.95 Shade approximately 95% ) = µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ 18. Day Care Tuition A random sample of 50 four-year-olds attending day care centers provided a yearly tuition average of $3987 and the population standard deviation of $630. Find the 90% confidence interval o fthe true (a) Step 1 Step Step 3 Find the confidence interval such that statistics calculator to P( X z α < µ < X + z α Shade approximately 90% ) = µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ (b) If a day care center were starting up and wanted to keep tuition low, what would be a reasonable amount to charge?

3 7.1 p. 379 # 7, 9, 18, 0, 1, 3, 5, 6 0. Length of Growing Season The growing seasons random sample of 35 U. S. cities were recorded, yielding a sample mean of days and the population standard deviation of 54. days. Estimate ll U. S. cities the true mean of the growing season with 95% confidence. Step 1 Step Step 3 Shade approximately 95% Find the confidence interval such that statistics calculator to P( X z α < µ < X + z α ) = µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ 1. Monthly Gasoline Expenditures How large a sample is needed to estimate the population mean monthly gasoline expenditure within $10 with 95% confidence? The population standard deviation is $ Step 1 Step Step 3 Shade approximately 95% to minimum sample size needed µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ

4 7.1 p. 379 # 7, 9, 18, 0, 1, 3, 5, 6 3. Birth Weights of Infants A health care professional wishes to estimate the birth weights of infants. How large a sample must be obtained if she desires to be 90% confident that the true mean is within ounces of the sample mean? Assume σ = 8 ounces. Step 1 Step Step 3 Shade approximately 90% to minimum sample size needed µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ 5. National Accounting Examination If the variance of a national accounting examination is 900, how large a sample is needed to estimate the true mean score within 5 points with 99% confidence? Step 1 Step Step 3 Shade approximately 99% to minimum sample size needed µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ

5 7.1 p. 379 # 7, 9, 18, 0, 1, 3, 5, 6 6. Undergraduate GPAs It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within 0.5 at the 99% confidence level? The population standard deviation is 1.. Step 1 Step Step 3 Shade approximately 99% to minimum sample size needed µ 3σ µ σ µ σ µ µ+σ µ+σ µ+3σ

6 7.1 p. 379 # 7, 9, 18, 0, 1, 3, 5, 6 Area Standard Normal Distribution Table z