1. Unit 8 Section 8-3

2. 8-3: z Test for a Mean  Many hypotheses are tested using the generalized statistical formula: Test value = (Observed Value)-(expected value) Standard error  z Test:  statistical test for the mean of a population  It can be used when n is greater than or equal to 30  It can also be used when the population is normally distributed and population standard deviation is known.  Formula :

3. Example 1: A researcher reports that the average salary of assistant professors is more than $42,000. A sample of 30 assistant professors has a mean salary of $43,260. At α = 0.05, test the claim that assistant professors earn more than $42,000 a year. The standard deviation of the population is $5230. Section 8-3

4. Summary: The sample mean is higher than the hypothesized population mean of $42,000, but it is not significantly higher. This means the difference may be due to chance. Remember : When the null hypothesis is not rejected there is still a probability of type II error. Also, just because we do not reject the null hypothesis, we cannot accept it as being true. Section 8-3

5. Example 2: A researcher claims that the average cost of men’s athletic shoes is less than $80. He selects a random sample of 36 pairs of shoes from a catalog and finds the following costs (in dollars). (The costs have been rounded to the nearest dollar). Is there enough evidence to support the researchers claim at α = 0.10. 607075558055 504080705095 1209075858060 1106580858545 756090906095 1108545907070 Section 8-3

6. Summary: The difference is significant. Remember : When the null hypothesis is rejected there is still a probability of type I error. Since α = 0.1, the probability of type I error is at most 10% (or 0.1). Section 8-3

7. Example 3: The Medical Rehabilitation Education Foundation reports that the average cost of rehabilitation for stroke victims is $24,672. To see if the average cost of rehabilitations is different at a particular hospital, a research selects a random sample of 35 stroke victims at a hospital and finds that the average cost of their rehabilitation is $25,226. The standard deviation of the population is $3251. At α = 0.01, can it be concluded that the average cost of stroke rehabilitation at a particular hospital is different from $24,672? Section 8-3

8. Remember: The claim can be either the null or the alternative hypothesis...therefore, it helps to identify which one is the claim. There are four possible outcomes from hypothesis testing: If H 0 is the claim If H 1 is the claim Section 8-3 Reject H 0 Do Not Reject H 0 There is enough evidence to reject the claim There is not enough evidence to reject the claim. Reject H 0 Do Not Reject H 0 There is enough evidence to support the claim There is not enough evidence to support the claim.

9. Homework:  Pg 414-415 : #’s 1 -7 ODD Section 8-3