Investigation 4: Sampling Distribution of the Sample Mean (P
Investigation 4: Sampling Distribution of the Sample Mean (P. 193-196)
Part 1: Sample Size of 40
Complete Procedure A as instructed. It will take the calculator several minutes to complete the command. While you are waiting, answer these questions:
i. Explain why it takes the calculator several minutes to complete the task. Your explanation should make direct references to some of the commands you entered in the calculator.
ii. Would you expect that the values you obtained in your list will be the same as the values obtained by other students? Explain.
After completing Procedure B, answer the following question:
iii. Explain what the first value in the table represents in the context of the river contaminant.
Procedure C
Compete the following table using the data from Step B. Construct a histogram on the grid provided below. Remember that this frequency distribution (histogram) will be used as a rough approximation of the sampling distribution of the mean.
|Class |Frequency |
|134 to 136 | |
|136 to 138 | |
|138 to 140 | |
|140 to 142 | |
|142 to 144 | |
|144 to 146 | |
|146 to 148 | |
|148 to 150 | |
|150 to 152 | |
|152 to 154 | |
|154 to 156 | |
|156 to 158 | |
|158 to 160 | |
|160 to 162 | |
iv. Compare your histogram to those of other students. Do you believe that the distribution of the sample mean is normally distributed? Explain.
Complete Procedure D as instructed and answer the following questions:
v. How does the mean of the sample means compare to the population mean of 147.3ppb? How do you think they would compare if you were able to obtain far more than 100 samples?
vi. Is the standard deviation of the 100 sample means approximately equal to the population standard deviation of 23.5ppb? Explain.
Procedure E
Divide the population standard deviation by [pic], where n is the sample size (40). Write the result below.
vii. Is the quotient approximately equal to the standard deviation of the sample means? Determine if this is correct for your data. Show all your work.
Part 2: Sample Size of 65
Complete Procedures A, B, and C.
|Class |Frequency |
|134 to 136 | |
|136 to 138 | |
|138 to 140 | |
|140 to 142 | |
|142 to 144 | |
|144 to 146 | |
|146 to 148 | |
|148 to 150 | |
|150 to 152 | |
|152 to 154 | |
|154 to 156 | |
|156 to 158 | |
|158 to 160 | |
|160 to 162 | |
i. Compare your histogram to those of other students. Do you believe that the distribution of the sample mean is normally distributed?
Complete Procedure D and answer the following question:
ii. How does the mean of the sample means compare to the population mean? How do you think they would compare if you were able to obtain far more than 100 samples?
Procedure E
Divide the population standard deviation by [pic], where n is the sample size (65).
iii. Is the quotient approximately equal to the standard deviation of the sample means? Determine if this is correct for your data. Show all your work.
Procedure F
How did the sample size affect the standard deviation of the sample mean?
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