Download Hypothesis Testing Practice Problems | Business Statistics II | STAT 202 and more Exams Business Statistics in PDF only on Docsity! Stat 202: Hypothesis Testing Practice Problems 1. Consider testing H0: µ ≥ 80 vs. H1: µ < 80 where µ is the mean of a normally distributed population having standard deviation σ = 15. The hypothesis will be tested at the α = 0.01 level of significance, using a sample of size n = 20. If in fact µ is equal to 72, what is the probability that the test will correctly reject the null hypothesis? In other words, find the power of the test at µ = 72. 2. (Based on text problem 11.37) A study has been conducted to examine the effectiveness of a new experimental program for preparing high school students for the SAT. Eighty students have been randomly divided into two groups of forty. One group receives the experimental program, and when they take the SAT the sample average score is equal to X = 1041.10 and the standard deviation of scores is 130.30. The second group receives a traditional program. They end up with an average score of X = 1012.48 with a standard deviation of 79.51. Does this result provide evidence that the new program is more effective than the traditional program? Test at the α = 0.05 level of significance. 3. (Based on text problem 11.69) A compressor manufacturer is testing two different designs for an air tank. Testing involves observing how much pressure a tank can withstand before it bursts. For a sample of four tanks of Design A, the average pressure to failure is 1400 psi with a standard deviation of 250 psi. For a sample of six tanks of Design B, the average pressure to failure is 1620 psi with a standard deviation of 230 psi. Test for a difference in mean pressure to failure for the two designs, at the α = 0.10 level of significance. Assume that the two populations of interest are normally distributed and have the same variance. 4. (Based on text problem 11.80) In an experiment comparing a new long-distance golf ball with the conventional design, each of 20 golfers hits one drive with each ball. For each golfer we calculate d = x1 – x2, where x1 is the distance the new ball is hit and x2 is the distance the old ball is hit. The average difference is calculated to equal 9.3, the standard deviation of differences is 10.5. Assuming that differences are normally distributed, test to see if the new ball goes further. Use α = 0.01.
