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Introductory Business Statistics

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Introductory Business StatisticsSolutions
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Table of contents
  1. Preface
  2. 1 Sampling and Data
    1. Introduction
    2. 1.1 Definitions of Statistics, Probability, and Key Terms
    3. 1.2 Data, Sampling, and Variation in Data and Sampling
    4. 1.3 Levels of Measurement
    5. 1.4 Experimental Design and Ethics
    6. Key Terms
    7. Chapter Review
    8. Homework
    9. References
    10. Solutions
  3. 2 Descriptive Statistics
    1. Introduction
    2. 2.1 Display Data
    3. 2.2 Measures of the Location of the Data
    4. 2.3 Measures of the Center of the Data
    5. 2.4 Sigma Notation and Calculating the Arithmetic Mean
    6. 2.5 Geometric Mean
    7. 2.6 Skewness and the Mean, Median, and Mode
    8. 2.7 Measures of the Spread of the Data
    9. Key Terms
    10. Chapter Review
    11. Formula Review
    12. Practice
    13. Homework
    14. Bringing It Together: Homework
    15. References
    16. Solutions
  4. 3 Probability Topics
    1. Introduction
    2. 3.1 Terminology
    3. 3.2 Independent and Mutually Exclusive Events
    4. 3.3 Two Basic Rules of Probability
    5. 3.4 Contingency Tables and Probability Trees
    6. 3.5 Venn Diagrams
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Bringing It Together: Practice
    12. Homework
    13. Bringing It Together: Homework
    14. References
    15. Solutions
  5. 4 Discrete Random Variables
    1. Introduction
    2. 4.1 Hypergeometric Distribution
    3. 4.2 Binomial Distribution
    4. 4.3 Geometric Distribution
    5. 4.4 Poisson Distribution
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  6. 5 Continuous Random Variables
    1. Introduction
    2. 5.1 Properties of Continuous Probability Density Functions
    3. 5.2 The Uniform Distribution
    4. 5.3 The Exponential Distribution
    5. Key Terms
    6. Chapter Review
    7. Formula Review
    8. Practice
    9. Homework
    10. References
    11. Solutions
  7. 6 The Normal Distribution
    1. Introduction
    2. 6.1 The Standard Normal Distribution
    3. 6.2 Using the Normal Distribution
    4. 6.3 Estimating the Binomial with the Normal Distribution
    5. Key Terms
    6. Chapter Review
    7. Formula Review
    8. Practice
    9. Homework
    10. References
    11. Solutions
  8. 7 The Central Limit Theorem
    1. Introduction
    2. 7.1 The Central Limit Theorem for Sample Means
    3. 7.2 Using the Central Limit Theorem
    4. 7.3 The Central Limit Theorem for Proportions
    5. 7.4 Finite Population Correction Factor
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  9. 8 Confidence Intervals
    1. Introduction
    2. 8.1 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size
    3. 8.2 A Confidence Interval for a Population Standard Deviation Unknown, Small Sample Case
    4. 8.3 A Confidence Interval for A Population Proportion
    5. 8.4 Calculating the Sample Size n: Continuous and Binary Random Variables
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  10. 9 Hypothesis Testing with One Sample
    1. Introduction
    2. 9.1 Null and Alternative Hypotheses
    3. 9.2 Outcomes and the Type I and Type II Errors
    4. 9.3 Distribution Needed for Hypothesis Testing
    5. 9.4 Full Hypothesis Test Examples
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  11. 10 Hypothesis Testing with Two Samples
    1. Introduction
    2. 10.1 Comparing Two Independent Population Means
    3. 10.2 Cohen's Standards for Small, Medium, and Large Effect Sizes
    4. 10.3 Test for Differences in Means: Assuming Equal Population Variances
    5. 10.4 Comparing Two Independent Population Proportions
    6. 10.5 Two Population Means with Known Standard Deviations
    7. 10.6 Matched or Paired Samples
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. Bringing It Together: Homework
    14. References
    15. Solutions
  12. 11 The Chi-Square Distribution
    1. Introduction
    2. 11.1 Facts About the Chi-Square Distribution
    3. 11.2 Test of a Single Variance
    4. 11.3 Goodness-of-Fit Test
    5. 11.4 Test of Independence
    6. 11.5 Test for Homogeneity
    7. 11.6 Comparison of the Chi-Square Tests
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. Bringing It Together: Homework
    14. References
    15. Solutions
  13. 12 F Distribution and One-Way ANOVA
    1. Introduction
    2. 12.1 Test of Two Variances
    3. 12.2 One-Way ANOVA
    4. 12.3 The F Distribution and the F-Ratio
    5. 12.4 Facts About the F Distribution
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  14. 13 Linear Regression and Correlation
    1. Introduction
    2. 13.1 The Correlation Coefficient r
    3. 13.2 Testing the Significance of the Correlation Coefficient
    4. 13.3 Linear Equations
    5. 13.4 The Regression Equation
    6. 13.5 Interpretation of Regression Coefficients: Elasticity and Logarithmic Transformation
    7. 13.6 Predicting with a Regression Equation
    8. 13.7 How to Use Microsoft Excel® for Regression Analysis
    9. Key Terms
    10. Chapter Review
    11. Practice
    12. Solutions
  15. A | Statistical Tables
  16. B | Mathematical Phrases, Symbols, and Formulas
  17. Index
1.

mean = 25 and standard deviation = 7.0711

3.

when the number of degrees of freedom is greater than 90

5.

df = 2

6.

a test of a single variance

8.

a left-tailed test

10.

H0: σ2 = 0.812;

Ha: σ2 > 0.812

12.

a test of a single variance

16.

a goodness-of-fit test

18.

3

20.

2.04

21.

We decline to reject the null hypothesis. There is not enough evidence to suggest that the observed test scores are significantly different from the expected test scores.

23.

H0: the distribution of AIDS cases follows the ethnicities of the general population of Santa Clara County.

25.

right-tailed

27.

2016.136

28.

Graph: Check student’s solution.

Decision: Cannot accept the null hypothesis.

Reason for the Decision: Calculated value of test statistics is either in or out of the tail of the distribution.

Conclusion (write out in complete sentences): The make-up of AIDS cases does not fit the ethnicities of the general population of Santa Clara County.

30.

a test of independence

32.

a test of independence

34.

8

36.

6.6

39.
Smoking level per day African American Native Hawaiian Latino Japanese Americans White Totals
1-10 9,886 2,745 12,831 8,378 7,650 41,490
11-20 6,514 3,062 4,932 10,680 9,877 35,065
21-30 1,671 1,419 1,406 4,715 6,062 15,273
31+ 759 788 800 2,305 3,970 8,622
Totals 18,830 8,014 19,969 26,078 27,559 10,0450
Table 11.54
41.
Smoking level per day African American Native Hawaiian Latino Japanese Americans White
1-10 7777.57 3310.11 8248.02 10771.29 11383.01
11-20 6573.16 2797.52 6970.76 9103.29 9620.27
21-30 2863.02 1218.49 3036.20 3965.05 4190.23
31+ 1616.25 687.87 1714.01 2238.37 2365.49
Table 11.55
43.

10,301.8

44.

right

46.
  1. Cannot accept the null hypothesis.
  2. Calculated value of test statistics is either in or out of the tail of the distribution.
  3. There is sufficient evidence to conclude that smoking level is dependent on ethnic group.
48.

test for homogeneity

50.

test for homogeneity

52.

All values in the table must be greater than or equal to five.

54.

3

57.

a goodness-of-fit test

59.

a test for independence

61.

Answers will vary. Sample answer: Tests of independence and tests for homogeneity both calculate the test statistic the same way ∑ (ij) (O-E) 2 E ∑ (ij) (O-E) 2 E . In addition, all values must be greater than or equal to five.

63.

true

65.

false

67.

225

69.

H0: σ2 ≤ 150

71.

36

72.

Check student’s solution.

74.

The claim is that the variance is no more than 150 minutes.

76.

a Student's t- or normal distribution

78.
  1. H0: σ = 15
  2. Ha: σ > 15
  3. df = 42
  4. chi-square with df = 42
  5. test statistic = 26.88
  6. Check student’s solution.
    1. Alpha = 0.05
    2. Decision: Cannot reject null hypothesis.
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: There is insufficient evidence to conclude that the standard deviation is greater than 15.
80.
  1. H0: σ ≤ 3
  2. Ha: σ > 3
  3. df = 17
  4. chi-square distribution with df = 17
  5. test statistic = 28.73
  6. Check student’s solution.
    1. Alpha: 0.05
    2. Decision: Cannot accept the null hypothesis.
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: There is sufficient evidence to conclude that the standard deviation is greater than three.
82.
  1. H0: σ = 2
  2. Ha: σ ≠ 2
  3. df = 14
  4. chi-square distribution with df = 14
  5. chi-square test statistic = 5.2094
  6. Check student’s solution.
    1. Alpha = 0.05
    2. Decision: Cannot accept the null hypothesis
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: There is sufficient evidence to conclude that the standard deviation is different than 2.
84.

The sample standard deviation is $34.29.

H0 : σ2 = 252
 Ha : σ2 > 252


df = n – 1 = 7.


test statistic: x 2 =  x 7 2 =  (n–1) s 2 25 2 =  (8–1) (34.29) 2 25 2 =13.169 x 2 =  x 7 2 =  (n–1) s 2 25 2 =  (8–1) (34.29) 2 25 2 =13.169 ;


Alpha: 0.05


Decision: Cannot reject the null hypothesis.


Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.


Conclusion: At the 5% level, there is insufficient evidence to conclude that the variance is more than 625.

87.
Marital status Percent Expected frequency
Never married 31.3 125.2
Married 56.1 224.4
Widowed 2.5 10
Divorced/Separated 10.1 40.4
Table 11.56
  1. The data fits the distribution.
  2. The data does not fit the distribution.
  3. 3
  4. chi-square distribution with df = 3
  5. 19.27
  6. 0.0002
  7. Check student’s solution.
    1. Alpha = 0.05
    2. Decision: Cannot accept null hypothesis at the 5% level of significance
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: Data does not fit the distribution.
89.
  1. H0: The local results follow the distribution of the U.S. AP examinee population
  2. Ha: The local results do not follow the distribution of the U.S. AP examinee population
  3. df = 5
  4. chi-square distribution with df = 5
  5. chi-square test statistic = 13.4
  6. Check student’s solution.
    1. Alpha = 0.05
    2. Decision: Cannot accept null when a = 0.05
    3. Reason for Decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: Local data do not fit the AP Examinee Distribution.
    5. Decision: Do not reject null when a = 0.01
    6. Conclusion: There is insufficient evidence to conclude that local data do not follow the distribution of the U.S. AP examinee distribution.
91.
  1. H0: The actual college majors of graduating females fit the distribution of their expected majors
  2. Ha: The actual college majors of graduating females do not fit the distribution of their expected majors
  3. df = 10
  4. chi-square distribution with df = 10
  5. test statistic = 11.48
  6. Check student’s solution.
    1. Alpha = 0.05
    2. Decision: Cannot reject null when a = 0.05 and a = 0.01
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: There is insufficient evidence to conclude that the distribution of actual college majors of graduating females fits the distribution of their expected majors.
94.

true

96.

false

98.

The hypotheses for the goodness-of-fit test are:

  1. H0: Surveyed obese fit the distribution of expected obese
  2. Ha: Surveyed obese do not fit the distribution of expected obese

Use a chi-square distribution with df = 4 to evaluate the data.

The test statistic is X2 = 9.85

The P-value = 0.0431

At 5% significance level, α = 0.05. For this data, P < α. Reject the null hypothesis.

At the 5% level of significance, from the data, there is sufficient evidence to conclude that the surveyed obese do not fit the distribution of expected obese.

100.
  1. H0: Car size is independent of family size.
  2. Ha: Car size is dependent on family size.
  3. df = 9
  4. chi-square distribution with df = 9
  5. test statistic = 15.8284
  6. Check student’s solution.
    1. Alpha: 0.05
    2. Decision: Cannot reject the null hypothesis.
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: At the 5% significance level, there is insufficient evidence to conclude that car size and family size are dependent.
102.
  1. H0: Honeymoon locations are independent of bride’s age.
  2. Ha: Honeymoon locations are dependent on bride’s age.
  3. df = 9
  4. chi-square distribution with df = 9
  5. test statistic = 15.7027
  6. Check student’s solution.
    1. Alpha: 0.05
    2. Decision: Cannot reject the null hypothesis.
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: At the 5% significance level, there is insufficient evidence to conclude that honeymoon location and bride age are dependent.
104.
  1. H0: The types of fries sold are independent of the location.
  2. Ha: The types of fries sold are dependent on the location.
  3. df = 6
  4. chi-square distribution with df = 6
  5. test statistic =18.8369
  6. Check student’s solution.
    1. Alpha: 0.05
    2. Decision: Cannot accept the null hypothesis.
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: At the 5% significance level, There is sufficient evidence that types of fries and location are dependent.
106.
  1. H0: Salary is independent of level of education.
  2. Ha: Salary is dependent on level of education.
  3. df = 12
  4. chi-square distribution with df = 12
  5. test statistic = 255.7704
  6. Check student’s solution.

  7. Alpha: 0.05

    Decision: Cannot accept the null hypothesis.

    Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.

    Conclusion: At the 5% significance level, there is sufficient evidence to conclude that salary and level of education are dependent.

108.

true

110.

true

112.
  1. H0: Age is independent of the youngest online entrepreneurs’ net worth.
  2. Ha: Age is dependent on the net worth of the youngest online entrepreneurs.
  3. df = 2
  4. chi-square distribution with df = 2
  5. test statistic = 1.76
  6. Check student’s solution.
    1. Alpha: 0.05
    2. Decision: Cannot reject the null hypothesis.
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: At the 5% significance level, there is insufficient evidence to conclude that age and net worth for the youngest online entrepreneurs are dependent.
114.
  1. H0: The distribution for personality types is the same for both majors
  2. Ha: The distribution for personality types is not the same for both majors
  3. df = 4
  4. chi-square with df = 4
  5. test statistic = 3.01
  6. Check student’s solution.
    1. Alpha: 0.05
    2. Decision: Cannot reject the null hypothesis.
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: There is insufficient evidence to conclude that the distribution of personality types is different for business and social science majors.
116.
  1. H0: The distribution for fish caught is the same in Green Valley Lake and in Echo Lake.
  2. Ha: The distribution for fish caught is not the same in Green Valley Lake and in Echo Lake.
  3. 3
  4. chi-square with df = 3
  5. 11.75
  6. Check student’s solution.
    1. Alpha: 0.05
    2. Decision: Cannot accept the null hypothesis.
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: There is evidence to conclude that the distribution of fish caught is different in Green Valley Lake and in Echo Lake
118.
  1. H0: The distribution of average energy use in the USA is the same as in Europe between 2005 and 2010.
  2. Ha: The distribution of average energy use in the USA is not the same as in Europe between 2005 and 2010.
  3. df = 4
  4. chi-square with df = 4
  5. test statistic = 2.7434
  6. Check student’s solution.
    1. Alpha: 0.05
    2. Decision: Cannot reject the null hypothesis.
    3. Reason for decision: Calculated value of test statistics is either in or out of the tail of the distribution.
    4. Conclusion: At the 5% significance level, there is insufficient evidence to conclude that the average energy use values in the US and EU are not derived from different distributions for the period from 2005 to 2010.
120.
  1. H0: The distribution for technology use is the same for community college students and university students.
  2. Ha: The distribution for technology use is not the same for community college students and university students.
  3. 2
  4. chi-square with df = 2
  5. 7.05
  6. p-value = 0.0294
  7. Check student’s solution.
    1. Alpha: 0.05
    2. Decision: Cannot accept the null hypothesis.
    3. Reason for decision: p-value < alpha
    4. Conclusion: There is sufficient evidence to conclude that the distribution of technology use for statistics homework is not the same for statistics students at community colleges and at universities.
122.
  1. The test statistic is always positive and if the expected and observed values are not close together, the test statistic is large and the null hypothesis will be rejected.
  2. Testing to see if the data fits the distribution “too well” or is too perfect.
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