Statistics for Engineering and the Sciences Practice Exam Questions Nazanin Naderi Visiting Assistant Professor University of Oklahoma Note 5 of 5E Example During periods of high electricity demand, especially during the hot summer months, the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by cooling the inlet air to the gas turbine. An increasingly popular cooling method uses high-pressure inlet fogging. The performance of a sample of 67 gas turbines was investigated. One measure of performance is heat rate and mean of heat rate of the 67 gas turbine is 11066 and SD is 1595. Suppose that a standard gas turbine has, on average, a heat rate of 10,000. Conduct a test to determine if the mean heat rate of gas turbines augmented with high-pressure inlet fogging exceeds 10,000. Use = 0.05. Note 5 of 5E Test of Hypothesis About a Population Mean Note 5 of 5E Example Refer to the study of the impact of calcium and gypsum on the flotation properties of silica in water, Fifty solutions of deionized water were prepared both with and without calcium/gypsum, and the level of flotation of silica in the solution was measured using a variable called zeta potential. The data are reproduced in the below table. Conduct a test of hypothesis to compare the mean zeta potential values of the two types of solutions. Can you conclude that the addition of calcium/gypsum to the solution impacts silica flotation level? = 0.1 Note 5 of 5E Testing the Difference Between Two Population Means: Independent Samples Note 5 of 5E Example A subcarrier can be classified as either a data subcarrier, a pilot subcarrier or a null subcarrier. In a sample of 1,024 subcarrier signals transmitted off the coast of Martha's Vineyard, 672 were determined to be data subcarriers, 256 pilot subcarriers, and 96 null subcarriers. Suppose a communications engineer who works near Martha's Vineyard believes that fewer than 70% of all subcarrier signals transmitted in the area are data subcarriers. Is there evidence to support this belief? Test using =0.05 Note 5 of 5E Testing a Population Proportion Note 5 of 5E Example In addition to the traditional bachelor of engineering (BE) degree, many universities worldwide offer a bachelor of technology (BTech) degree for students who wish to work as an engineering technician. There is a perception that BTech students are not as \"academically strong\" as BE students. The researchers compared BE and Btech students at a Australian university on a variety of academic-related outcomes. The following table gives the percentages of BE and BTech students who withdrew from two traditionally rigorous courses, engineering mathematics and engineering graphics/CAD. Note 5 of 5E Example a. Is there sufficient evidence of a difference between the percentage of BE students and percentage of Btech students who withdraw from engineering mathematics? Test using =0.05. Is there sufficient evidence of a difference between the percentage of BE students and percentage of Btech students who withdraw from engineering graphics/ CAD? Test using =0.05. Note 5 of 5E . b. Testing the Difference Between two Population Proportions Note 5 of 5E Example A company produces a fast drying rubber cement in 32-ounce aluminum cans. A quality control inspector is interested in testing whether the variance of the amount of rubber cement dispensed into the cans is more than .3. If so, the dispensing machine is in need of adjustment. Since inspection of the canning process requires that the dispensing machines be shut down, and shutdowns for any lengthy period of time cost the company thousands of dollars in lost revenue, the inspector is able to obtain a random sample of only 10 cans for testing. After measuring the weights of their contents, the inspector computes the following summary statistics: =31.55 s=0.48 Does the sample evidence indicate that the dispensing machines are in need of adjustment? Test at =0.05 Note 5 of 5E Example study of deep hole drilling under drill chip congestion. Test to determine whether the true standard deviation of drill chip lengths differs from 75 mm. for n=51 drill chips, s=50.2. Test at =0.05. Note 5 of 5E Testing a Population Variance Note 5 of 5E Normal Table Note 5 of 5E Chi- Square Table Note 5 of 5E Chi- Square Table Note 5 of 5E