1. 1 Business 90: Business Statistics Professor David Mease Sec 03, T R 7:30-8:45AM BBC 204 Lecture 24 = Start Chapter “Fundamentals of Hypothesis Testing: One-Sample Tests” (FOHT) Agenda: 1) Go over Homework 8 2) Assign Homework 9 (due Thursday 5/13) 3) Announcement: No class or office hours Thursday 4) Start Chapter FOHT 5) Take quiz over Homework 8

2. 2 Homework 8 – Due Tuesday 5/4 1) Read chapter entitled “Confidence Interval Estimation” but only sections 1, 2 and 4 2) In that chapter do textbook problems 2, 12, 16, 32 and 42 3) A random sample of 8 SJSU students is taken. The ages of the students are 19,23,30,30,45,25,24,20 a. Using this data give a 90% confidence interval for the mean age of all SJSU students. Do NOT use Excel. b. If a sample of 8 students is taken every year, how often will the resulting 90% confidence intervals contain the true population mean? c. Are your answers to A and B correct even if the population of ages for the students is not normal? Why or why not? d. Use Excel to check your answer for Part A. 4) a. Everything else being equal, which will be narrower: a 90% confidence interval or a 95% confidence interval? b. Everything else being equal, which will be narrower: a confidence interval using a sample size of 1000 or a confidence interval using a sample size of 10,000? c. Everything else being equal, which will be narrower: a confidence interval where the standard deviation is 10 or a confidence interval where the standard deviation is 3?

3. 3 1) Read chapter entitled “Fundamentals of Hypothesis Testing: One-Sample Tests” but only sections 1, 2 and 3. 2) In that chapter do textbook problems 42 (parts a, c and d) and 44 (parts a, c and d). (In 42 the alternative hypothesis is that the mean is less than 2.8, and in 44 the alternative hypothesis is that the mean is less than 8.) 3) Redo/practice/study In Class Exercises #101, #102 and #103. Homework 9 – Due Thursday 5/13

4. 4 Announcement: This Thursday 5/6 is a furlough day so there will be no class and no office hours.

5. 5 Fundamentals of Hypothesis Testing: One-Sample Tests Statistics for Managers Using Microsoft ® Excel 4 th Edition

6. 6 Chapter Goals After completing this chapter, you should be able to: Formulate null and alternative hypotheses for applications involving a single population mean Know how to use the p-value approach to test the null hypothesis

7. 7 In class exercise #100: A consumer group claims that a nation-wide fast food chain has less than 4 ounces of beef in their quarter pound hamburger. To investigate this claim, they take a sample of 36 hamburgers and observe that the mean weight in this sample is 3.28 ounces. Assume that the population standard deviation is 2 ounces. A) If the population mean weight were really 4 ounces, what is the probability of getting a sample of 36 with a mean weight as low as was observed in this sample? B) Based on the data, do you think that the fast food chain is lying about the weight of their hamburgers?

8. 8 Table 2

9. 9 What is a Hypothesis? A hypothesis is a claim (assumption) about a population parameter: population mean Example: The mean weight of all hamburgers sold is greater than or equal to 4 ounces

10. 10 States the assumption (numerical) to be tested Is always about a population parameter, not about a sample statistic Begin with the assumption that the null hypothesis is true Similar to the notion of innocent until proven guilty Refers to the status quo Always contains “=”, “≤” or “  ” sign May or may not be rejected The Null Hypothesis, H 0

11. 11 The Alternative Hypothesis, H 1 It is the hypothesis the researcher is trying to establish Is the opposite of the null hypothesis e.g., The mean weight of all hamburgers sold is less than 4 ounces ( H 1 : μ < 4 ) Challenges the status quo Never contains the “=”, “≤” or “  ” sign May or may not be proven Is generally the hypothesis that the researcher is trying to prove

12. 12 Sampling Distribution of X μ = 4 If H 0 is true If it is unlikely that we would get a sample mean of this value...... then we reject the null hypothesis that μ  4. Reason for Rejecting H 0 3.28... if in fact this were the population mean… X

13. 13 Level of Significance,  Defines the unlikely values of the sample statistic if the null hypothesis is true Is designated by , (level of significance) Typical values are.01,.05, or.10 Is selected by the researcher at the beginning We reject the null hypothesis if the probability of observing a test statistic as extreme or more extreme than what we observed if the null hypothesis were true is less than 

14. 14 Convert Sample Statistic (e.g., ) to Test Statistic (e.g., Z statistic ) Obtain the p-value from a the normal table (or Excel) (The p-value is the probability of observing a test statistic as extreme or more extreme than what was observed if the null hypothesis were true) Compare the p-value with  If p-value is less than , reject H 0 If p-value is greater than , do not reject H 0 p-Value Approach to Testing X

15. 15 Convert Sample Statistic (e.g., ) to Test Statistic (e.g., Z statistic ) Obtain the p-value from a the normal table (or Excel) (The p-value is the probability of observing a test statistic as extreme or more extreme than what was observed if the null hypothesis were true) Compare the p-value with  If p-value is less than , reject H 0 If p-value is greater than , do not reject H 0 p-Value Approach to Testing X The direction of “extreme” is defined by the alternative hypothesis

16. 16 In class exercise #101: A consumer group claims that a nation-wide fast food chain has less than 4 ounces of beef in their quarter pound hamburger. To investigate this claim, they take a sample of 36 hamburgers and observe that the mean weight is 3.28 ounces. Assuming that the population standard deviation is 2 ounces, test the null hypothesis that the mean is at least 4 ounces at the 5% significance level. Null Hypothesis:Alternative Hypothesis: P-value: Decision: Conclusion:

17. 17 In class exercise #102: SJSU claims that the average age of its students is 24. One student felt that this number was too low, and took a sample of 20 students for which the mean age was 25.7. Assuming that the population standard deviation is 5 years, test the alternative hypothesis that the mean age is greater than 24 at the 1% significance level. Null Hypothesis: Alternative Hypothesis: P-value: Decision: Conclusion: