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Business Research Methods William G. Zikmund

Business Research Methods William G. Zikmund. Chapter 21: Univariate Statistics . Univariate Statistics. Test of statistical significance Hypothesis testing one variable at a time. Hypothesis. Unproven proposition Supposition that tentatively explains certain facts or phenomena

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Business Research Methods William G. Zikmund

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  1. Business Research MethodsWilliam G. Zikmund Chapter 21: Univariate Statistics

  2. Univariate Statistics • Test of statistical significance • Hypothesis testing one variable at a time

  3. Hypothesis • Unproven proposition • Supposition that tentatively explains certain facts or phenomena • Assumption about nature of the world

  4. Hypothesis • An unproven proposition or supposition that tentatively explains certain facts or phenomena • Null hypothesis • Alternative hypothesis

  5. Null Hypothesis • Statement about the status quo • No difference

  6. Alternative Hypothesis • Statement that indicates the opposite of the null hypothesis

  7. Significance Level • Critical probability in choosing between the null hypothesis and the alternative hypothesis

  8. Significance Level • Critical Probability • Confidence Level • Alpha • Probability Level selected is typically .05 or .01 • Too low to warrant support for the null hypothesis

  9. The null hypothesis that the mean is equal to 3.0:

  10. The alternative hypothesis that the mean does not equal to 3.0:

  11. A Sampling Distribution m=3.0

  12. A Sampling Distribution a=.025 a=.025 m=3.0

  13. A Sampling Distribution UPPER LIMIT LOWER LIMIT m=3.0

  14. Critical values ofm Critical value - upper limit

  15. Critical values ofm

  16. Critical values ofm Critical value - lower limit

  17. Critical values ofm

  18. Region of Rejection LOWER LIMIT m=3.0 UPPER LIMIT

  19. Hypothesis Test m =3.0 2.804 3.78 m=3.0 3.196

  20. Type I and Type II Errors Accept null Reject null Null is true Correct- no error Type I error Null is false Type II error Correct- no error

  21. Type I and Type II Errors in Hypothesis Testing State of Null Hypothesis Decision in the Population Accept Ho Reject Ho Ho is true Correct--no error Type I error Ho is false Type II error Correct--no error

  22. Calculating Zobs

  23. Alternate Way of Testing the Hypothesis

  24. Alternate Way of Testing the Hypothesis

  25. Choosing the Appropriate Statistical Technique • Type of question to be answered • Number of variables • Univariate • Bivariate • Multivariate • Scale of measurement

  26. NONPARAMETRIC STATISTICS PARAMETRIC STATISTICS

  27. t-Distribution • Symmetrical, bell-shaped distribution • Mean of zero and a unit standard deviation • Shape influenced by degrees of freedom

  28. Degrees of Freedom • Abbreviated d.f. • Number of observations • Number of constraints

  29. or Confidence Interval Estimate Using the t-distribution

  30. Confidence Interval Estimate Using the t-distribution = population mean = sample mean = critical value of t at a specified confidence level = standard error of the mean = sample standard deviation = sample size

  31. Confidence Interval Estimate Using the t-distribution

  32. Hypothesis Test Using the t-Distribution

  33. Univariate Hypothesis Test Utilizing the t-Distribution Suppose that a production manager believes the average number of defective assemblies each day to be 20. The factory records the number of defective assemblies for each of the 25 days it was opened in a given month. The mean was calculated to be 22, and the standard deviation, ,to be 5.

  34. Univariate Hypothesis Test Utilizing the t-Distribution The researcher desired a 95 percent confidence, and the significance level becomes .05.The researcher must then find the upper and lower limits of the confidence interval to determine the region of rejection. Thus, the value of t is needed. For 24 degrees of freedom (n-1, 25-1), the t-value is 2.064.

  35. Univariate Hypothesis Test t-Test

  36. Testing a Hypothesis about a Distribution • Chi-Square test • Test for significance in the analysis of frequency distributions • Compare observed frequencies with expected frequencies • “Goodness of Fit”

  37. Chi-Square Test

  38. Chi-Square Test x² = chi-square statistics Oi = observed frequency in the ith cell Ei = expected frequency on the ith cell

  39. Chi-Square Test Estimation for Expected Number for Each Cell

  40. Chi-Square Test Estimation for Expected Number for Each Cell Ri = total observed frequency in the ith row Cj = total observed frequency in the jth column n = sample size

  41. Univariate Hypothesis Test Chi-square Example

  42. Univariate Hypothesis Test Chi-square Example

  43. Hypothesis Test of a Proportion p is the population proportion p is the sample proportion p is estimated with p

  44. Hypothesis Test of a Proportion p = H : . 5 0 p ¹ H : . 5 1

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