THE MORE T-DISTRIBUTION & SIGNIFICANCE TESTING FOR QUANTITATIVE DATA CHAPTER 23

HYPOTHESIS TESTING FOR MEANS (QUANTITATIVE DATA)

THE SAME 5 STEPS NO MATTER THE DATA TYPE: Common Steps to all Significance Tests: 1) State Ho and Ha. 2) Specify significance level, . 3) Identify correct test and conditions. 4) Calculate the value of the test statistic 5) Find the P-value for the observed data (If the P-value is less than or = to , the test result is “statistically significant at level .) 6) Answer the question in context.

WRITING HYPOTHESES To test the hypothesis: Ho:  =  o and H a :  >  o H a :  <  o H a :    o Calculate the test statistics t and the p value. These have the same meanings as they did for proportions. We make the same conclusions based on p-values and alpha.

CONDITIONS: The conditions for hypothesis testing are the same as they were for confidence intervals when the data is quantitative.

DO THE MATH:

WRITING YOUR CONCLUSION: Remember your two possible conclusions: If p value < α, With a p-value of ___ < α at ____, we can reject the null & can support _____(the alternative in context). If p-value > α, With a p-value of ___ > α at ____, we fail to reject the null and we can not support that _____ (the alternative in context).

EXAMPLE 1 Last year the number of false fire alarms in a large city averaged 10.4 a day. In an effort to reduce this number, the fire department conducted a safety program in the city’s schools. Six months after completion of the program, a sample of 21 days had a mean of 8.1 false alarms and a standard deviation of 3.4. Does it appear that the fire department’s program is successful?

EXAMPLE 2 A new blood pressure drug is advertised to reduce a patient’s blood pressure an average of 10 units after a week of medication. Blood pressure reductions were recorded for 37 patients after treatment with the drug for 1 week. The patients had a mean reduction in blood pressure of 8.7 units with a standard deviation of 5.1 units. Is there evidence to dispute the advertised claim from the drug’s manufacturer?

EXAMPLE 3 The mean yield of corn in the United States is about 120 bushels per acre. A survey of 50 farmers this year gives a sample mean yield of x-bar = bushels per acre with a standard deviation of s x = 10 bushels per acre. We want to know whether this is good evidence that the national mean this year is not 120 bushels per acre. Assume that the farmers surveyed are an SRS from the population of all commercial corn growers. Are you convinced that the population mean is not 120 bushels per acre?

EXAMPLE 4 A pharmaceutical manufacturer does a chemical analysis to check the potency of its products. The standard release potency for cephalothin crystals is 910 ppm. An SRS of 16 lots gives the following potency data: You want to know if the cephalothin crystals have lost potency during shipping and storage.

EXAMPLE 5 The manufacturer of an over-the-counter pain reliever claims that the product brings pain relief to headache sufferers in less than 3.5 minutes, on average. In order to be able to make this claim in its television advertisements, the manufacturer was required by a particular television network to present statistical evidence in support of the claim. The manufacturer reported that for a random sample of 50 headache sufferers, the mean relief time was 3.3 minutes with a standard deviation of 1.1 minutes. Do the data support the manufacturers claim? Test using a significance level of 5%.