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1 FUNDAMENTALS of HYPOTHESIS TESTING

### Transcript of Fundamentals of Hypothesis Testing

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FUNDAMENTALS of HYPOTHESIS TESTING

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Errors in Decision Making

Possible Hypothesis Test Outcomes

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Actual Situation

Decision H0 True H0 False

Do Not Reject H0

No ErrorProbability 1 - α

Type II ErrorProbability β

Reject H0 Type I ErrorProbability α

No ErrorProbability 1 - β

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SOAL:

1. A random sample of size 20, from a normal population, has mean = 182 and s = 2.3. Test

With α = 0.05

2. Heights were measured for 12 plants grown under the treatment of a particular nutrient. The sample mean and standard deviation of those measurements were and 10 inches, respectively.

3. Measurements of the acidity (pH) of rain samples were recorded at 13 sites in an industrial region.

3.5 5.1 5.0 3.6 4.8 3.6 4.7 4.3 4.2 4.5 4.94.7 4.8

Determine a 95% confidence interval for the mean acidity of rain in that

region.

4. A physical model suggests that the mean temperature increase in the water used as coolant in a compressor chamber should not be more than 50 C. Temperature increases in the coolant measured on 8 independent runs of the compressing unit revealed the following data:6.4 4.3 5.7 4.9 6.5 5.9 6.4 5.1a. Do the data contradict the assertion of the physical model? (Test at

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α=0.05) State the assumption you make about the population.

b. Determine a 95% confidence interval for the mean increase of the

temperature in the coolant.

5. The average weekly earnings for all full-time –equivalent employees are reported to be \$344.Suppose that you want to check this claim sice you believe it is too low. You want to prove that average weekly earnings of all employees are higher that the amount stated. You collect a random sample of 1,200 employees in all areas and find that sample mean is \$361 and the sample standard deviation \$110. Can you didisprove the claim?

6. According to Money, the average amount of money that a typical person in the United States would need to make him or her feel rich is \$1.5 million. A researcher wants to test this claim. A random sample of 100 people in the United States reveales that their mean “ amount to feel rich” is \$2.3 milion and the standard deviation is \$0.5 milion. Conduct the test.