 # Statistics Questions

## Transcribed Text

QUESTION 1: As a consumer, you are curious about variation in power consumption of electronic devices. Testing of 2 dehumidifiers recorded variance in power consumption (in units of kW). 28 tests of the first dehumidifier yielded a sample standard deviation of 52.6 kW and 26 tests of the second dehumidifier yielded a sample standard deviation of 84.2 kW. Is there a difference in variance of power consumption between these dehumidifiers? 1. 2. 3. 4. 5. 6. 7. QUESTION 2: The lifetime of a product is normally distributed with a population mean thought to be 10 and a population standard deviation known to be 1.3. We wish to test: Ho: = 10 versus H1: 10 with a sample of 13 specimens. a) i) If the acceptance region is defined as 9.5 X <10.5, find the type / error probability ii) Provide a sketch to indicate how the acceptance region is defined. iii) Based on answer in i) above, is this a "valuable" product (such as a pacemaker): briefly explain. b) i) It seems we got the lifetime wrong: Find ß for the case where the true mean is 10.7 ii) Provide a sketch to indicate how ß is calculated. ii) How might we have been so wrong ie 10.7 VS 10: briefly explain? c) Can type / error be reduced by increasing sample size: briefly explain? d)Can type Il error be reduced by increasing sample size: briefly explain? QUESTION 3: Two methods have been developed to determine the nickel content of steel. Data is represented below. It is known that the population variances are equal: based on this, is there a difference in determination of mean nickel content with these methods (at the 5% level)? Nickel Content via Method 1 (%): 3.18, 3.14, 2.75, 3.10 Nickel Content Method 2 (%) : 3.19, 3.29, 3.01, 3.26 1. 2. 3. 4. 5. 6. 7. QUESTION 4: Laminated films are intended to be produced with a mean thickness of 1.1 millimeters. 2 different devices are used for this purpose and the standard deviations of device 1 and device 2 have been recorded as 01 =0.025 millimeters and O2 =0.015 millimeters. Samples from each machine are measured for thickness and the data is below. Is there any evidence to support the claim that these devices are producing different mean thicknesses ( a =0.05)? Device 1 (mm): 1.18, 1.14, 1.05, 1.10 Device 2 (mm): 1.19, 1.29, 1.01, 1.06 1. 2. 3. 4. 5. 6. 7. QUESTION 5: Two new mathematical simulation techniques are tested by measuring run time on a computer (each run taken under identical conditions). The results are shown in the list below. Is there evidence to support the claim that technique 2 is faster (less time taken) than technique 1 (a =0.05)? Run 1 Run 2 Run 3 Time for Technique 1 (sec) 51 55 56 Time for Technique 2 (sec) 48 52 49 1. 2. 3. 4. 5. 6. 7.

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