Confidence Intervals Cases PDF

Confidence Intervals Dr. Srilakshminarayana G Confidence Intervals for  when  is Unknown- The t Distribution A (1-)100% confidence interval for  when  is not known (assuming a normally distributed population) is given by: s...

Confidence Intervals Dr. Srilakshminarayana G Confidence Intervals for  when  is Unknown- The t Distribution A (1-)100% confidence interval for  when  is not known (assuming a normally distributed population) is given by: s x t n  2 where t is the value of the t distribution with n-1 degrees of 2  freedom that cuts off a tail area of 2 to its right. Airtel Calls Jio wants to estimate the average length of long-distance calls during weekends. A random sample of 560 calls gives a mean minutes and standard deviation s=11.96 minutes. Give a 95% confidence interval and a 90% confidence interval for the average length of a long- distance phone call during weekends.  Insurance Frauds An insurance company handling malpractice cases is interested in estimating the average amount of claims against physicians of a certain specialty. The company obtains a random sample of 265 claims and finds $19,530 and s=$7,542. Give a 95% confidence interval and a 99% confidence interval for the average amount of a claim.  According to ABC International, the average cost of a domestic trip for business travelers in the financial industry is $1,250. Suppose another travel industry research company takes a random sample of 51 business travelers in the financial industry and determines that the sample average cost of a domestic trip is $1,192, with a sample standard deviation of $279. Construct a 98% confidence interval for the population mean from these sample data. Assume that the data are normally distributed in the population. Now go back and examine the $1,250 figure published by ABC International. Does it fall into the confidence interval computed from the sample data? What does it tell you?  A valve manufacturer produces a butterfly valve composed of two semicircular plates on a common spindle that is used to permit flow in one direction only. The semicircular plates are supplied by a vendor with specifications that the plates be 2.37 millimeters thick and have a tensile strength of five pounds per millimeter. A random sample of 20 such plates is taken. Electronic calipers are used to measure the thickness of each plate; the measurements are given here. Assuming that the thicknesses of such plates are normally distributed, use the data to construct a 95% level of confidence for the population mean thickness of these plates. What is the point estimate? How much is the error of the interval?  Some fast-food chains offer a lower-priced combination meal in an effort to attract budget- conscious customers. One chain test-marketed a burger, fries, and a drink combination for $1.71. The weekly sales volume for these meals was impressive. Suppose the chain wants to estimate the average amount its customers spent on a meal at their restaurant while this combination offer was in effect. An analyst gathers data from 28 randomly selected customers. The following data represent the sample meal totals.  How much experience do supply-chain transportation managers have in their field? Suppose in an effort to estimate this, 41 supply-chain transportation managers are surveyed and asked how many years of managerial experience they have in transportation. Survey results (in years) are shown below. Use these data to construct a 99% confidence interval to estimate the mean number of years of experience in transportation. Assume that years of experience in transportation is normally distributed in the population.  According to the Stern Marketing Group, 9 out of 10 professional women say that financial planning is more important today than it was five years ago. Where do these women go for help in financial planning? Forty- seven percent use a financial advisor (broker, tax consultant, financial planner). Twenty-eight percent use written sources such as magazines, books, and newspapers. Suppose these figures were obtained by taking a sample of 560 professional women who said that financial planning is more important today than it was five years ago. Construct a 95% confidence interval for the proportion of professional women who use a financial advisor. Use the percentage given in this problem as the point estimate.  The highway department wants to estimate the proportion of vehicles on Interstate 25 between the hours of midnight and 5:00 A.M. that are 18- wheel tractor trailers. The estimate will be used to determine highway repair and construction considerations and in highway patrol planning. Suppose researchers for the highway department counted vehicles at different locations on the interstate for several nights during this time period. Of the 3,481 vehicles counted, 927 were 18-wheelers. a. Determine the point estimate for the proportion of vehicles traveling Interstate 25 during this time period that are 18-wheelers. b. Construct a 99% confidence interval for the proportion of vehicles on Interstate 25 during this time period that are 18-wheelers.  What proportion of commercial airline pilots are more than 40 years of age? Suppose a researcher has access to a list of all pilots who are members of the Commercial Airline Pilots Association. If this list is used as a frame for the study, she can randomly select a sample of pilots, contact them, and ascertain their ages. From 89 of these pilots so selected, she learns that 48 are more than 40 years of age. Construct a 95% confidence interval to estimate the population proportion of commercial airline pilots who are more than 40 years of age.