Statistics Practice Problems - Prof. James Davenport, Study notes of Statistics

Download Statistics Practice Problems - Prof. James Davenport and more Study notes Statistics in PDF only on Docsity! Practice Problems # 08 1. Gravel pieces are classified as small, medium, or large. A vendor claims that at least 10% of the gravel pieces from her plant are large. In a random sample of 1600 pieces, 150 pieces were classified as large. Is this enough evidence to reject the claim? 2. A new gun-like apparatus has been created by a medical engineer to replace the needle in administering vaccines. The apparatus, which is connected to a large supply of the vaccine, can be set to inject different amounts of the serum, but the variance in the amount of serum injected to a given person must not be greater than .06 to ensure proper inoculation. A random sample of twenty-five injections resulted in a sample variance of 0.135 (i.e. s2 = 0.135). a. Find a 90% confidence interval for the true variance σ2. b. Does is matter whether or not the sample (the 25 observations used in this experiment) is a random sample from a normally distributed population? Explain. c. Do the data provide evidence to indicate the gun is not working properly? To answer this question, interpret the confidence interval computed in part a. as an interval of plausible values for the unknown parameter σ2. 3. Measurements of ammonium concentrations (in mg/L) at a large number of wells were made in the stat of Iowa. These included 349 alluvial wells and 143 quaternary wells. The concentrations in the alluvial wells gave a sample average of 0.27, and the assumed population standard deviation for alluvial wells is σ1 = 0.40. Those at the quaternary wells have a sample average of 1.62 with σ2 = 1.70. Find a 95% confidence interval for the difference in mean concentration between alluvial and quaternary wells. 4. The carbon content (in parts per million – ppm) was measured five times for each of two different silicon wafers. The measurements were as follows: Wafer A: 1.10 1.15 1.16 1.10 1.14 Wafer B: 1.20 1.18 1.16 1.18 1.15 Test the hypothesis that the two means are equal using the Welch’s T’ and α = 0.01.