1. Part IV – Hypothesis Testing Chapter 4 Statistics for Managers Using Microsoft Excel, 7e © 2014 Pearson Prentice-Hall, Inc. Philip A. Vaccaro, PhD MGMT E-5070

2. Requirements 7. Compute the coefficient of correlation ( r ). 8. Set up a 95% and 99% confidence interval estimate of the average annual sales volume in a city in which eight ( 8 ) ads are broadcast daily. 9. At the a =.01 and.05 level of significance, is there a relationship between sales volume and the number of radio ads broadcast? 10. Set up the 99% confidence interval estimate of the true slope. 11. Discuss why you should not predict annual sales volume in a city which has fewer than 7 broadcasts daily or more than 14 daily.

32. Hypothesis Testing: σ Known, the ‘p’- Value Approach  The p-value is the probability of obtaining a test statistic equal to or more extreme ( ) than the observed sample value given H 0 is true  Also called observed level of significance*  Smallest value of  for which H 0 can be rejected * Because we can reject or not reject Ho “at a glance“.

33. Hypothesis Testing: σ Known p-Value Approach  Convert Sample Statistic (ex. X) to Test Statistic (ex. ‘Z’ statistic or ‘t’ statistic )  Obtain the ‘p’-value from a table or by using Excel  Compare the p-value with   If p-value < , reject H 0  If p-value  , do not reject H 0

34. Hypothesis Testing: σ Known p-Value Approach Example: How likely is it to see a sample mean of 2.84 or something lower, or 3.16 or something higher from the mean, if the true mean is  = 3.0 ? translated to a Z scores : p-value =.0228 +.0228 =.0456.0228  /2 =.025 -1.960 -2.0 Z1.96 2.0.0228  /2 =.025 Z0.00 - 2.00.0228 Z0.00 + 2.00.9772 Z = 2.84 - 3.00.8 √100 = -.16 = - 2.00.08 Z = 3.16 - 3.00.8 √100 = +.16 = + 2.00.08 Ho: μ = 3.00 2.84 3.16 (.9772)

35. Hypothesis Testing: σ Known p-Value Approach  Compare the p-value with   If p-value < , reject H 0  If p-value  , do not reject H 0 Here: p-value =.0456  =.05 Since.0456 <.05, you reject the null hypothesis that μ = 3.0.0228  /2 =.025 -1.960 -2.0 Z1.96 2.0.0228  /2 =.025 The probability of seeing a sample mean of 2.84 or less, or 3.16 or more from the mean, if the population mean is really 3.0 is only 4.56%

36. Requirements 7. Compute the coefficient of correlation ( r ). 8. Set up a 95% and 99% confidence interval estimate of the average annual sales volume in a city in which eight ( 8 ) ads are broadcast daily. 9. At the a =.01 and.05 level of significance, is there a relationship between sales volume and the number of radio ads broadcast? 10. Set up the 99% confidence interval estimate of the true slope. 11. Discuss why you should not predict annual sales volume in a city which has fewer than 7 broadcasts daily or more than 14 daily.

38. Part IV – Hypothesis Testing Chapter 4 Statistics for Managers Using Microsoft Excel, 7e © 2014 Pearson Prentice-Hall, Inc. Philip A. Vaccaro, PhD MGMT E-5070