Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Unit 8 Section 8-3 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: z = X -m s n Section 8-3 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 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 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. 60 50 120 110 75 110 70 40 90 65 60 85 75 80 75 80 90 45 55 70 85 85 90 90 80 50 80 85 60 70 55 95 60 45 95 70 Section 8-3 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 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 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 H0 is the claim Reject H0 Do Not Reject H0 There is enough evidence to reject the claim There is not enough evidence to reject the claim. If H1 is the claim Reject H0 There is enough evidence to support the claim Do Not Reject H0 There is not enough evidence to support the claim. Section 8-3 Homework: Pg 414-415: #’s 1 -7 ODD