HYPOTHESIS TESTING

HYPOTHESIS TESTING

HYPOTHESIS TESTINGPrepared by: Paolo BautistaThings to add: Relationship between Est and HT; How to compute the p-values; Example 7; consolidate with exercise sheet.1PreliminariesWe wish to test whether a particular assumption/claim regarding the population is true or not.Null Hypothesis (H0) original assumptionAlternative Hypothesis (H1) Determine a critical value to determine whether or not to reject HoHT : PLBautistaErrorsType I Error reject H0 when in fact it is trueType II Error fail to reject H0 when it is falseNull Hypothesis is TrueNull Hypothesis is FalseFail to RejectCorrect DecisionType II Error ()RejectType I Error ()Correct DecisionHT : PLBautistaSteps in Hypothesis TestingWrite the null and alternative hypotheses.Indicate the level of significance.Determine the critical value/s.Compute the test statistic.Decide the conclusion of the test.HT : PLBautistaHYPOTHESIS TESTINGOne PopulationTwo PopulationsOne MeanCase 1Case 2One ProportionOne VarianceDifference of Two MeansCase 1 to 3Paired MeansDifference of Two ProportionsDifference of Two VariancesHT : PLBautistaTesting for One MeanCase 1: is known, or n 30Z-test will be used

HT : PLBautistaTesting for One MeanThe test statistic is given by

HT : PLBautistaExample 1A manufacturer of sports equipment has developed a new synthetic fishing line that he claims has a mean breaking strength of 8 kilograms with a standard deviation of 0.5 kilograms. Test the hypothesis that = 8 kg against the alternative that 8 kg if a random sample of 50 lines is tested and found to have a mean breaking strength of 7.8 kg. Use a 0.01 level of significance.HT : PLBautistaIdentify the proper hypothesesThe manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotels accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of weekend guest bills to test the managers claim.The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period.HT : PLBautistaIdentify the proper hypothesesA production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling.Because of high production-changeover time and costs, a director manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $220 per hour. A research study will measure the cost of the new method over a sample production period.

HT : PLBautistaCase 2: unknown, AND n < 30t-test will be used

The t-values have n 1 degrees of freedomThe test statistic is given by

HT : PLBautistaExample 2Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 liters. Use a 0.01 level of significance and assume that the distribution of contents is normal.

HT : PLBautistaTesting for One ProportionZ-test will be usedThe test statistic is given by

HT : PLBautistaExample 3A commonly prescribed drug on the market for relieving nervous tension is believed to be only 60% effective. Experimental results with a new drug administered to a random sample of 100 adults who were suffering from nervous tension showed that 70 received relief. Is this sufficient evidence to conclude that the new drug is superior to the one commonly prescribed? Use a 0.05 level of significance.HT : PLBautistaTesting for One VarianceA chi-square test will be used

The test statistic is given by

HT : PLBautistaExample 4A manufacturer of car batteries claims that the life of his batteries has a variance equal to 0.81 years. If a random sample of 10 of these batteries have a variance of 1.44 years, is there evidence that the variance exceeds 0.81 a year? Use a 0.05 level of significance HT : PLBautistaTesting the Difference of Two MeansCase 1:Z-test will be usedThe test statistic is given by:

HT : PLBautistaExample 5A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by less than 12 kilograms. To test this claim, 50 pieces of each type of thread are tested under similar conditions. Type A thread had an average tensile strength of 86.7 kilograms with a standard deviation of 6.28 kilograms, while type B thread had an average tensile strength of 77.8 kilograms with a standard deviation of 5.61 kilograms. Test the manufacturers claim using a 0.05 level of significance.HT : PLBautistaCase 2: 1=2 unknown, AND n1