# Eight questions on Statistics

Please see the attached file.

1. Identify the type of sampling (random, stratified, systematic, cluster, convenience) used in each of the following AND state whether the sample results are likely to reflect the population from which the sample was drawn. (3 points each)

a. ______________________ Each hundredth hamburger manufactured is checked to determine its fat content.

b. ______________________ Mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes. Then 10 are selected from each groups and interviewed to determine whether they have been bitten by a dog in that last year.

2. Seven runners ran a race, their times (in minutes) to complete it were as follows: Determine the indicated values.

8 11 13 7 6 8 10

a) variance s2=

b) standard deviation s=

3. A psychologist developed a test intended to measure the aggressiveness of drivers. The scores on the test have a mean of 250 and a standard deviation of 93. Is a score of 630 unusual? Why or why not?

4. A professor gives two different versions of a test. Version A results in scores with a mean of 78 and a standard deviation of 16. Version B results in scores with a mean of 52 and a standard deviation of 12. Which score is relatively better: 70 on Version A, or 50 on Version B? Explain your choice.

5. The ages of 20 dancers who responded to a call to audition for a musical comedy are listed in the box below. Use the raw data set to answer the listed questions.

a) Find Q2 for the data.

b) What is the 30th percentile?

c) Would you use the Empirical Rule or Chebyshev's Theorem to describe the distribution of this data? Explain your choice.

d) What percent of this data set is within two standard deviations of the mean?

e) If you were to group the data into classes using the interval 17 to 21 as the first class how many data would be in the third class?

6. Given the following frequency table:

Absences Frequency Relative

Frequency Cumulative

Frequency

0-9 25

10-19 36

20-29 71

30-39 40

40-49 28

a. What is the class width?

b. Fill in Relative and Cumulative Frequencies on the chart above.

c. What is the mean of the data?

7. If the variance of a set of data is 36, what is the standard deviation? ___________

8. The empirical rule states that if a distribution is bell-shaped approximately 95% of the data values fall with 2 standard deviations of the mean. The mean price of houses in a certain neighborhood is $90,000 and the standard deviations $10,000. Find the price range for which at least 95% of the houses will sell.

#### Solution Preview

See attached file.

1. Identify the type of sampling (random, stratified, systematic, cluster, convenience) used in each of the following AND state whether the sample results are likely to reflect the population from which the sample was drawn. (3 points each)

a. ______________________ Each hundredth hamburger manufactured is checked to determine its fat content.

Answer: Systematic Sampling

In systematic sampling, elements are selected from the population at uniform interval that is measured in time, order or space. Here every hundredth hamburger manufactured is being checked.

The sample results are likely to reflect the population from which the sample was drawn. This is because the sample would be representative of the population.

b. ______________________ Mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes. Then 10 are selected from each groups and interviewed to determine whether they have been bitten by a dog in that last year.

Answer: Stratified Sampling

In stratified sampling the population is divided into relative homogeneous groups or strata. Then elements are selected from each stratum at random. Here the strata are based on gender and according to whether they walk or ride on their routes.

The sample results are likely to reflect the population from which the sample was drawn. This is because the sample would be representative of the population. However proper weights would have to be given to the sample statistics (depending on the size of the different strata), before estimating the population parameters.

2. Seven runners ran a race, their times (in minutes) to complete it were as follows: Determine the indicated values.

8 11 13 7 6 8 10

a) variance s2= 6

b) standard deviation s= 2.45

X= X 2 =

8 64

11 121

13 169

7 49

6 36

8 64

10 100

Total= 63 603

n=no of observations= 7

Mean= 9 =63/7

variance={ΣX 2 - n(Mean) 2 }/(n-1)= 6 =(603-7*9^2)/(7-1)

standard deviation =√Variance= 2.45 =√6

3. A psychologist developed a test intended to measure the aggressiveness of drivers. The scores on the test have a mean of 250 and a standard deviation of 93. Is a score of 630 unusual? Why or why not?

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#### Solution Summary

Answers to 8 questions on sampling, random, stratified, systematic, cluster, convenience, variance, standard deviation, normal distribution, quartile, percentile, Chebyshev's Theorem, frequency table, class width, Relative frequency, Cumulative Frequency, mean.