Practice Problems 6 on Applied Statistics for Engineers and Scientists | STAT 541, Assignments of Statistics

Download Practice Problems 6 on Applied Statistics for Engineers and Scientists | STAT 541 and more Assignments Statistics in PDF only on Docsity!

Practice Problems # 06

1. Interpolation methods are used to estimate heights above sea level for locations where direct measurements are unavailable. In the article “Transformation of Ellipsoid Heights to Local Leveling Heights” (M. Yanalak and O. Baykal, Journal of Surveying Engineering, 2001:90- 103), a second-order polynomial method of interpolation for estimating heights from GPS measurements is evaluated. In a sample of 74 locations, the errors made by the method had a sample average of 3.8 cm, with a sample standard deviation of 4.8 cm.

a. Find a 98% confidence interval for the population mean error made by this method. b. Approximately how many locations must be sampled so that a 95% confidence interval will specify the mean to within + 0.7 cm.

2. Based on tests conducted on a LARGE sample of welded joints, a 90% confidence interval for the mean Rockwell B Hardness of a certain type of weld was computed to be (83.2 , 84.1). Find a 95% confidence interval for the mean Rockwell B Hardness of this type of weld.
3. A soft-drink manufacturer purchases aluminum cans from an outside vendor. A random sample of 70 cans is selected from a large shipment, and each is tested for strength by applying an increasing load to the side of the can until it punctures. Of the 70 cans, 52 meet the specification for puncture resistance.

a. Find a 95% confidence interval for the proportion of cans in the shipment that meet the specification. b. Find the sample size needed for a 95% confidence interval to specify the proportion within + 0.05.

4. Five measurements are taken of the octane rating for a particular type of gasoline. Assume these are a simple random sample from the population of this type of gasoline, and that the distribution of measurements is a normally distributed population. The results (in%) are 87.0, 86.0, 86.5, 88.0, 85.3; find a 95% confidence interval for the mean octane rating for this type of gasoline.