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Practice Final Exam - Basic Statistics | MS 204, Exams of Statistics

Jacksonville State University (JSU)Statistics
Prof. Janice L. Case

Material Type: Exam; Professor: Case; Class: Basic Statistics; Subject: Mathematics (MS); University: Jacksonville State University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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MS 204 Statistics Practice Exam
Forbes Magazine lists the richest people in the world each year. The following data represents the ages
of 40 of these individuals. All of these individuals have a net worth of at least $5 billion.
17 24 31 32 32 43 43 43
46 50 51 51 54 55 55 59
59 60 62 62 62 62 63 64
69 71 71 73 73 74 75 75
76 77 79 81 82 82 84 84
1. Choose an appropriate graph to describe this data and draw your graph below. Justify your choice
by explaining what information is given by your graph.
2. Calculate the mean and median age. Is one of these measures better than the other in describing central
tendency? Why or why not?
3. Calculate the standard deviation for age. What information is given by this statistic?
4. Use this sample of 40 billionaires to construct a 95% confidence interval for the mean age of all
billionaires.
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MS 204 Statistics Practice Exam

Forbes Magazine lists the richest people in the world each year. The following data represents the ages of 40 of these individuals. All of these individuals have a net worth of at least $5 billion. 17 24 31 32 32 43 43 43 46 50 51 51 54 55 55 59 59 60 62 62 62 62 63 64 69 71 71 73 73 74 75 75 76 77 79 81 82 82 84 84

  1. Choose an appropriate graph to describe this data and draw your graph below. Justify your choice by explaining what information is given by your graph.
  2. Calculate the mean and median age. Is one of these measures better than the other in describing central tendency? Why or why not?
  3. Calculate the standard deviation for age. What information is given by this statistic?
  4. Use this sample of 40 billionaires to construct a 95% confidence interval for the mean age of all billionaires.
  1. Based on past information, an analyst has hypothesized that billionaires are getting younger. He believes that the mean age of billionaires is now less than 65. a. State the null and alternative hypotheses which would be used to test the research hypothesis that the mean age is less than 65. b. Use a significance level of  = .05. What is the rejection region? c. Calculate the test statistic using your sample mean and standard deviation from the previous page. Consider the 40 individuals to be a sample of all billionaires. d. Is there enough evidence to reject the null hypothesis? e. What conclusion can be drawn about the age of billionaires? f. Find the p-value for your test statistic. g. Do the test statistic and the p-value lead to the same conclusion?

7. Minitab was used to generate 200 random samples of size 50 from a population that has a normal distribution

with mean 55 and standard deviation of 15. From the descriptive statistics and the histogram, what can you

conclude about the mean, standard deviation, and shape of the sampling distribution?

  1. 0 53. 8 54. 6 55. 4 56. 2 57. 0 95 % Confidence Interval for Mu
  2. 6 54. 7 54. 8 54. 9 55. 0 55. 1 55. 2 55. 3 55. 4 55. 5 95 % Confidence Interval for Median

Variable: C 201

Maximum 3 rd Quartile Median 1 st Quartile Minimum

N

Kurtosis Skewness Variance StDev Mean P-Value: A-Squared:

  1. 5030

95 % Confidence Interval for Median 95 % Confidence Interval for Sigma 95 % Confidence Interval for Mu Anderson-Darling Normality Test

Descriptive Statistics

8. The American Heart Association recommends that an individual’s cholesterol level be under 200 milligrams

per 100 milliliters. Cholesterol readings of 16 women under age 40 were randomly selected from the

Framingham Heart Study. The following output resulted from a test of the alternative hypothesis that the

mean reading was less than 200.

Test of mu = 200 vs mu < 200

Variable N Mean StDev SE Mean

level 16 197.69 20.71 5.

Variable 95.0% Upper Bound T P

level 206.76 -0.45 0.

a. Using a significance level of α = .05, what conclusion is drawn concerning mean cholesterol level?

b. What would a Type II Error be in the context of this problem?

  1. The boxplot below describes the salaries in $ hundred thousands for executive officers of a company. Comment on the central tendency, variability, and shape of the distribution.

S a la ry

  1. The following regression analysis was performed on Minitab to investigate the relationship between salary (x) and absences (y) for state employees. In hypothesis testing for regression, the null hypothesis is that there is no linear relationship. The alternative hypothesis is that there is a linear relationship. Find the p-value and comment on whether the relationship between salary and absences is significant at the .05 level.

The regression equation is

Absences (y) = 3.82 - 0.0720 Salary (x)

Analysis of Variance

Source DF SS MS F P

Regression 1 1.9440 1.9440 27.31 0.

Residual Error 7 0.4982 0.

Total 8 2.