Statistical Analysis of Mean Differences and Confidence Intervals - Prof. Dinesh Sharma, Quizzes of Mathematics

Download Statistical Analysis of Mean Differences and Confidence Intervals - Prof. Dinesh Sharma and more Quizzes Mathematics in PDF only on Docsity! 1. You are testing H0 : µ = 10 vs Ha : µ < 10 based on a random sample of 20 observations from a normal distribution. The data gave ȳ = 8, s = 4. The value of the t statistic is a.-0.5 b. -10 c.-2.24 answer: c. t = 8−10 4/ √ 20 = −2.24. 2. You are testing H0 : µ = 10 vs Ha : µ < 10 based on a random sample of 20 observations from a normal distribution. The t statistic is -2.25. The p-value of the test is (0.0182). R code: pt(-2.25,19). 3. Data on the blood cholesterol levels of 24 rats (milligrams per deciliter of blood) give ȳ = 85, s = 12. A 95% CI for the mean blood cholesterol of rats is a. 79.9 to 90.1 b. 80.2 to 89.8 c.84.0 to 86.0. answer : a. 85± 2.069 ∗ 12/ √ 24 = (79.9, 90.1). 4. The following is a summary of stress limit for specimens using two types of wood. Wood Type sample size sample mean sample sd Red Oak 15 8.50 0.80 Fir 15 7.70 1.25 Assume the two population variances are different. Use smaller sample size-1 as the degrees of freedom. What t critical value will you use in getting a 90% CI for the difference between the average stress limit for red oak and for fir? t=1.761. The 90% CI is from 8.5− 7.7± 1.761 √ 0.802/15 + 1.252/15 = (0.13, 1.47). Test whether the true average stress limit for red oak is different from that for fir. 1