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

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.

Hypothesis Testing: σ Known ,the ‘p’- Value Approach

The p-value is the probability of obtaining a test statistic equal to or more extreme ( < or > ) than the observed sample value given H0 is true Also called observed level of significance* Smallest value of for which H0 can be rejected

* Because we can reject or not reject Ho “at a glance“ .

Hypothesis Testing: σ Knownp-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 H0

If p-value , do not reject H0

Hypothesis Testing: σ Knownp-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

-1.96 0-2.0

Z1.962.0

.0228

/2 = .025

Z 0.00

- 2.00 .0228

Z 0.00

+ 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)

Hypothesis Testing: σ Knownp-Value Approach

Compare the p-value with If p-value < , reject H0

If p-value , do not reject H0

Here: p-value = .0456 = .05

Since .0456 < .05, you reject the null hypothesis that μ = 3.0

.0228

/2 = .025

-1.96 0

-2.0

Z1.96

2.0

.0228

/2 = .025

The probabilityof seeing a

sample meanof 2.84 or less,

or 3.16 or more from

the mean, ifthe population

mean is really 3.0

is only 4.56%

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.

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