Assignment:
1. Assume the managers for a manufacturer of trash bags wish to initiate a quality test that will alert the production manager to stop the equipment when the bags are statistically determined to be too weak. The population mean weight the bag should hold is 50 pounds and the population standard deviation is known to be 1.6 pounds. The test will use a random sample of bags and the average of the sample will be computed. The managers decide the risk of a Type I error should be set at 0.05 and the risk of a Type II error should be set at 0.02. The bags will be considered weak when the mean weight the bag holds is below 50 pounds.
a. State the null and alternative hypotheses.
b. Clearly describe the Type I error in the context of this exercise.
c. Clearly describe the Type II in the context of this exercise.
2. A snake physiologist investigates the effects of temperature on the heart rate of juniper pythons. He selects 9 specimens of approximately the same age, size, and sex. He placed each animal at a preselected temperature between 2o and 18o Celcius at measured their heart rates. He wants to predict heart rate of the python based on the temperature. Here are the results:
Temperature (in Degrees Celcius)
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Temperature (in Degrees Celcius)
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Heart Rate (in beats per minte)
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2
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5
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4
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11
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6
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11
|
|
8
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14
|
|
10
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22
|
|
12
|
23
|
|
14
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32
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16
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29
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18
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32
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a. Find SSxx, SSyy, and SSxy
b. Find the slope and y intercept using the results for the formulas in part a. Interpret the results.
c. Find the equation of the least squares regression line that predicts the heart rate of a python based on his preselected temperature using the formulas given in class.
d. Use the least squares regression line to predict the heart rate of a snake with a temperature of 15 Celcius.
e. Find the correlation coefficient using the formula given in class. Interpret the correlation coefficient.
f. Find the coefficient of determination. Interpret the coefficient of determination.
3. The average U.S. daily internet use at home is one hundred and forty minutes. A sample of 64 homes in Soddy-Daisy showed an average usage of one hundred and seventy minutes with a standard deviation of 80 minutes. We are interested in determining whether or not the average usage in SoddyDaisy is significantly different from the U.S. average.
a. State the null and alternative hypotheses to be tested.
b. Find the 95% confidence interval for the population mean usage.
c. Using only the confidence interval above, test the hypothesis and state the conclusion in the context of the situation given.
4. A random sample of 36 people has been collected to determine if holiday spending is more or less this year than it has been in the past. In the past, holiday spending has been normally distributed with a mean of $300. The collected data are as follows: mean spending: $267, sample standard deviation: $80.
a. What are the null and alternative hypotheses?
b. Calculate the appropriate test statistic.
c. Find the p-value.
d. Using a 0.01 level of significance, make a decision based on the p-value and interpret it in the context of the situation given. What conclusion does your decision lead you to regarding holiday spending this year?
5. Listed below are measured amounts of lead (in micrograms per cubic meter or mg/m^3 ) in the air. The EPA has established an air quality standard for lead: 1.5 mg/m^3 . The measurements shown below were recorded at the World Trade Center on different days immediately following the destruction caused by the terrorist attacks on September 11, 2001. At α=.05, test the claim that the sample is from a population with a mean greater than the EPA standard of 1.5mg/m^3 .
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5.40
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1.10
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0.42
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0.73
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0.48
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1.10
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a. State the null hypothesis
b. State the rejection region associated with this test. Include the appropriate degrees of freedom.
c. Calculate the test statistic.
d. Explain your conclusion after comparing the test statistic to the critical point in the context of the situation given.