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# difference between a sample and population mean/standard

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Why is there a difference between a sample and population mean/standard deviation or a sample and population proportion? how accurately does the "sample" you discussed represent the actual or potential "population" of data? What steps can you take to improve the probability that decisions you make based on the sample will be reliable and valid in the future, in other locations, or with other people?

#### Solution Preview

Why is there a difference between a sample and population mean/standard deviation or a sample and population proportion?

The population mean is the average of all the items in the full population. The sample mean is the average of the subset that you pulled as a sample. The standard deviation of the population is how much variance from the mean is found in the population and the standard deviation of the sample is the amount of variance from the mean in the subset you pulled as a sample. Similarly, the proportion in the population is the proportion in everyone while the proportion in the sample is just the proportion ...

#### Solution Summary

Your tutorial is 330 words in everyday language and discusses how samples differ from populations and some ways to ensure that your results are generalizable to the population.

\$2.19

## Mean, Range, Standard Deviation, Confidence Interval Calculations

Assume the following sample data:

LENGTH (FT) SAMPLE 1
207.495 247.725 345.33 257.175
198.855 166.185 326.295 233.01
209.25 177.12 173.07 180.36
252.315 182.655 186.975 233.955
192.915 216 250.95 207.09
209.25 312.12 209.25 247.725

1. Calculate and explain the sample mean.
2. Calculate and explain the standard deviation.
3. Calculate and explain the range.
4. Calculate the 95% confidence interval for the mean.
5 Determine if the sample size is adequate to study the population if you assume E=50 FT.

6. Determine the probability of a sample point being between 250 - 300 FT.
7. Determine the probability of a sample point being between 175 - 200 FT.
8. Discuss differences between descriptive and inferential statistics.
9. Discuss the differences between a population and a sample.
10. Distinguish a parameter from a statistic.

By hand, perform a one sample t test to determine if this sample (above sample 1) could have come from a population where the population mean = 245 feet.

11. H0:
12. H1
13. t CRITICAL:
14. t CALCULATED:
15. DECISION
16. EXPLANATION OF DECISION

LENGTH (FT) SAMPLE 2
210.495 253.725 349.33 260.175
204.855 170.185 329.295 233.01
210.25 188.12 183.07 189.36
260.315 190.655 196.975 243.955
199.915 231 250.95 217.09
215.25 312.12 215.25 252.725

Use Excel to perform a two sample t test to determine if this sample (above SAMPLE 2) could have come from the same population that the sample in the previous question (SAMPLE 1) came from.

17. H0:
18. H1:
19. t CRITICAL
20. t CALCULATED:
21. DECISION:
22. EXPLANATION OF DECISION
23. p VALUE AND ITS MEANING

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