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# Statistical Concepts

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Part A: What is dispersion? Briefly name five measures of dispersion. Describe the characteristics of the standard deviation. Explain!

Part B: Briefly describe to what kind of data does Chebyshev's Theorem apply? To what kind of data does Empirical Rule apply? Explain.

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#### Solution Preview

RESPONSE:

Part A: What is dispersion? Briefly name five measures of dispersion. Describe the characteristics of the standard deviation. Explain!

DISPERSION

Dispersion refers to an important characteristic of a data set. The data values in a sample are not all the same. This variation between values is called dispersion. When the dispersion is large, the values are widely scattered; when it is small they are tightly clustered. The width of diagrams such as dot plots, box plots, stem and leaf plots is greater for samples with more dispersion and vice versa (http://www.stats.gla.ac.uk/steps/glossary/presenting_data.html#mode).

In other words, dispersion is how the data is distributed, and the measures of dispersion measure how far each element is from some measure of central tendency (average). There are several ways to measure the variability of the data. There are ...

#### Solution Summary

This solution explains the concept of dispersion, including five measures of dispersion. It describes the characteristics of the standard deviation. Then, it briefly describes the type of data that Chebyshev's Theorem and to The Empirical Rule applies to.

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## Problems on Basic Statistical Concepts

I need some help on answer these questions with workings: (See attached file for full problem description)
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1) What is the best point estimate of the
a) population parameter?
b) population variance?

2) A sample of 100 elements produced a mean of 48 and a standard deviation
of 8. Find the 99% confidence interval for the population mean. Hint - this is a large sample.

3) A recent study of 28 city residents showed that the mean of the time they had lived at their present address was 9.3 years. The standard deviation of the sample was 2 years. Find the 90% confidence interval of the true mean.

4) A university dean wishes to estimate the average number of hours his part-time instructors teach per week. The standard deviation from a previous study is 2.6 hours. How large a sample must be selected if he wants to be 99% with a maximum error of one hour.

5) An employment counselor found that in a sample of 100 unemployed workers, 65% were not interested in returning to work. Find the 95% confidence interval of the true proportion of workers who do not wish to return to work.

6) A nutritionist wishes to determine, within 3%, the true proportion of adults who do not eat any lunch. If he wishes to be 95% confident that it contains the population proportion, how large a sample will be necessary? A previous study found that 15% of the 125 people surveyed said they did not eat lunch.

7) A tektronics dental X-ray machine bears a label stating that the machine gives radiation dosages with a mean of less then 8 milliroentgens. Sample data consists of 66 randomly selected observations with a mean of 7.13 milliroentgens and a standard deviation of 1.61 milliroentgens. Using a .01 level of significance, test the claim stated on the label.

a. State the claim:
b. Is this a one-tailed test or a two-tailed test?
c. What are the two decisions that can be made in a hypothesis test?
d. In simple terms, describe a Type I error:
e. In simple terms, describe a Type II error:
f. Identify the probability of making a Type I error:

8) The Dengue Fever medication, H76 bears a label indicating the presence of 600 mg of acetaminophen in each fluid ounce of the drug. The FDA randomly selected 75 one-ounce samples and found that the mean acetaminophen content is 579mg and the standard deviation is 20 mg. Using a .01 level of significance, test the claim of Monkey Pharmaceutical Company that the population mean is equal to 600 mg.

a. State the claim:
b.
c. Test Statistic:
d. Decision:
e. Conclusion:

Would you buy this medication? Why or why not?

9) A health club manager claims that members lose an average of 15 pounds during the first six months of membership. A sample of fifteen members of the club showed they lost an average of 11.5 pounds during the first six months of membership with a standard deviation of 2.2 pounds. Test at the 5% significance level if the mean weight loss during the first six months of their membership by all members of this health club is less than 15 pounds.
a. State the claim:
b.
c. Test Statistic:
d. Decision:
e. Conclusion:

10). A department store manager claims that at least 45% of persons who visit this store make a purchase. In a sample of 400 persons who visited this store, 37% made a purchase. Test at the 5% significance level if the claim of the management is true.
a. State the claim:
b.
c. Test Statistic:
d. Decision:
e. Conclusion:
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