Week+5+discussion+1



__**9.59**__ **:****THE CIGARETTE ADVERTISEMENT CASE**

Recall that the cigarette industry requires that models in cigarette ads must appear to be at least 25 years old. Also recall that a sample of 50 people is randomly selected at a shopping mall. Each person in the sample is shown a “typical cigarette ad” and is asked to estimate the age of the model in the ad.
 * a:** Let //μ// be the mean perceived age estimate for all viewers of the ad, and suppose we consider the industry requirement to be met if //μ// is at least 25. Set up the null and alternative hypotheses needed to attempt to show that the industry requirement is not being met.
 * b:** Suppose that a random sample of 50 perceived age estimates gives a mean of years and a standard deviation of //s// = 3.596 years. Use these sample data and critical values to test the hypotheses of part //α// at the .10, .05, .01, and .001 levels of significance.
 * c:** How much evidence do we have that the industry requirement is not being met?
 * d:** Do you think that this result has practical importance? Explain your opinion.

Answers:

a. //H//0 : μ ≥ 25 versus //H//1 : μ 25 b. //t// = −2.63. Reject //H//0 at all α’s except .001. c. Since //p-// value = .0057, reject //H//0 at all α’s except .001; very strong evidence. d. The result has practical importance because x bar is more than 1.3 years which is under 25

(Bowerman, Bruce.. //Essentials of Business Statistics, 4th Edition//. McGraw-Hill Learning Solutions, 2012. p. 379). 

Discussion 2 Consider the cigarette ad situation discussed in Exercise 9.59. Using the sample information given in that exercise, the //p//-value for testing //H//0 versus //Ha// can be calculated to be .0057.
 * 9.60:** **THE CIGARETTE ADVERTISEMENT CASE**
 * a:** Determine whether //H//0 would be rejected at each of //α// = .10, //α// = .05, //α// = .01, and //α// = .001.
 * b:** Describe how much evidence we have that the industry requirement is not being met.

Answers:

If we do not know the standard deviation, we can base a hypothesis test about mu on the sampling distribution. We use critical values and p-values to perform a t test about a population mean when s is unknown.
 * a.** Reject H0 at // a // = .10, .05, .01, but not at // a // = .001.
 * b.** Very strong evidence

(Bowerman, Bruce.. //Essentials of Business Statistics, 4th Edition//. McGraw-Hill Learning Solutions, 2012. p. 379). 