CHAPTER 8 Hypothesis TestingStat 200 – Elementary StatisticsIntroductionSection 8.1 Steps in Hypothesis Testing- Traditional MethodStating the Null and Alternative HypothesisPossible Outcomes of a Hypothesis TestCritical ValuesOne-Tailed TestSection 8.2 Z Test for a MeanExample 1Example 2Outcomes of a Hypothesis-TestingExample 4Chi-Square Test for Single VarianceStat 200 – Elementary Statistics IntroductionHypothesis testing In hypothesis testing, the researcher must define:1.2.3. 4.5.6.7.Methods to Test Hypotheses1.2.3.Section 8.1 Steps in Hypothesis Testing- Traditional MethodA statistical hypothesis is a conjecture about a population parameter which may or may not be true.There are two types of statistical hypotheses for each situation: 1. Student NotesCHAPTER 8 Hypothesis Testing2.Null hypothesis, symbolized by ____, is a statistical hypothesis that states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters.Alternative hypothesis, symbolized by ______, is a statistical hypothesis that states the existence of a difference between a parameter and a specific value, or states that there is a difference between two parameters.Stating the Null and Alternative HypothesisSituation AWill the pulse rate of a patient increase, decrease, or remain unchanged after acertain medication is taken? The mean pulse rate of the population is 82 beatsper minute.Situation BAn additive is to increase the life of an automobile battery. If the mean lifetime of the battery without the additive is 36 months, then the hypotheses areSituation CA contractor wishes to lower heating bills by using a special type of insulation in houses. If theaverage of the monthly heating bills is $78, her hypotheses about heating costs with the use ofinsulation areExample 1State the null and alternative hypotheses for each:a. A researcher thinks that if expectant mothers use vitamin pills, the birth weight of the babies will increase. The average birth weight of the population is 8.6 pounds.b. An engineer hypothesizes that the mean number of defeats can be decreased in a manufacturing process of compact disks by using robots instead of humans for certain tasks. The mean number of defective disks per 1000 is 18.c. A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean of the scores was 73.Statistical test Test valuePossible Outcomes of a Hypothesis TestSummary of Possible OutcomesType I error Type II error  and  ProbabilitiesCritical ValuesThe critical or rejection region is the range of values of the test value that indicates that there is a significant difference and that the null hypothesis should be rejected.The noncritical or nonrejection region is the range of values of the test value that indicates that the difference was probably due to chance and that the null hypothesis should not be rejected.One-Tailed TestTwo-Tailed TestExample 2Find the critical value(s) for each situation and draw the appropriate figure.a.A left tailed test with a = 0.10b.A two-tailed test with a = 0.02c.A right tailed test with a = 0.005Hypothesis-Testing (Traditional Method)1.2.3.4.5.Section 8.2 Z Test for a Meanz test Example 1A 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 a = 0.05, test the claim that assistant professors earn more than $42,000 a year. The standard deviation of the population is $5230.Example 2A 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 the catalog and finds the following costs. Is there enough evidence to support the researcher’s claim at a = 0.10.60 70 75 55 80 55 50 40 80 70 50 95120 90 75 85 80 60 110 65 80 85 85 4575 60 90 90 60 95 110 85 45 90 70 70Example 3A Medical Foundation reports that the average cost of rehabilitation for stroke victims is $24,672. To see if the average cost of rehabilitation is different at a particular hospital, a researcher selects a random sample of 35 stroke victims at the hospital and finds that the average cost of their rehabilitation is $25,226. The standard deviation of the population is $3251. At a = 0.05, can it be concluded that the average cost of stroke rehabilitation at a particular hospital is different from $24,672?Outcomes of a Hypothesis-TestingI. Claim is H0III. Claim is H1P-value Decision Rule When Using a P-ValueExample 4A researcher wishes to test the claim that the average are of lifeguards in Ocean City is greaterthan 24 years. She selects a sample of 36 guards and finds the mean of the sample to be 24.7years, with a standard deviation f 2 years. Is here evidence to support the claim at a = 0.05? Use the P-value method.Example 5A researcher claims that the average wind speed in a certain city is 8 miles per hour. A sampleof 32 days has an average wind speed of 8.2 miles per hour. The standard deviation of the sample is 0.6 mile per hour. At a = 0.05, is there enough evidence to support the claim? Use the P-value method.Section 8.3 t test for a Meant testThe formula for the t test is:The degrees of freedom are d.f. = n–1.Example 1tXs na. Find the critical t value for a = 0.05 with d.f. = 16 for a right-tailed t test.b. Find the critical t value for a = 0.01 with d.f. = 22 for a left-tailed t test.c. Find the critical t value for a = 0.10 with d.f. = 18 for a two-tailed t test.d. Find the critical t value for a = 0.05 with d.f. = 28 for a right-tailed t test.Example 2A job placement director claims that the average starting salary for nurses is $24,000. A sample of 10 nurse’s salaries has a mean of $23,450 and a standard deviation of $400. Is there enough evidence to reject the director’s claim at a = 0.05?Step 1:Step 2:Step 3:Step 4:Step 5:Example 3An educator claims that the average salary of substitute teachers in a certain school district isless than $60 per day. A random sample of eight districts is selected, and the daily salaries areshown. Is there enough evidence to support the educator’s claim at a = 0.10?60 56 60 55 70 55 60 55Step