Section 8-3 Testing a Claim about a Proportion Example:

Transcription

1 Section 8-3 Testing a Claim about a Proportion Example: A research center claims that more than 55% of US adults regularly watch network news broadcast. To test the claim, a random sample of 425 adults was asked whether they regularly watched network news broadcast, and 255 said yes. At 0. 05, is there enough evidence to support the claim? 1

2 In a Gallup poll of 1012 randomly selected adults, 9% said that cloning of humans should be allowed. Use a 0.05 significance level to test the claim that less than 10% of all adults say human cloning should be allowed. Can a newspaper run a headline that less than 10% of all adults approve of cloning of humans? 2

3 In a recent year, of the 109,857 arrests for federal offenses, 29.1% were for drug offenses (based on the data from the Department of Justice). Use a 0.01 significance level to test the claim that the drug offense rate is equal to 30%. How can the result be explained, given that 29.1% appears to be so close to 30%? 3

4 Section 8-4 Testing a Claim about a Mean ( known) Example: The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of lb. Assuming that is known to be lb, use a 0.10 significance level to test the claim that the population mean of all such bear weights is less than 200 lb. 4

5 A random sample of 100 babies is obtained and the mean head circumference is found to be 40.6 cm. Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean head circumference of all 2-month old babies is equal to 40.0 cm. 5

6 Section 8-5 Testing a Claim about a Mean ( unknown) Note: Assume a normal distribution for the population for each example in this section. Example: The sugar content (grams of sugar per gram of cereal) for a sample of different cereals was taken. Those amounts are summarized with these statistics: n = 16, x g, s g. Use a 0.05 significance level to test the claim that the mean sugar content for all cereals is less than 0.3 g. 6

7 Claim: The mean starting salary for college graduates who have taken a statistics course is equal to $46,000. Sample data: n = 27, x $45, 678, s $ Test at the significant level

8 The Carolina Tobacco Company advertised that its best-selling non-filtered cigarettes contain at most 40 mg of nicotine, but Consumer Advocate magazine ran tests of 10 randomly selected cigarettes and found the amounts (in mg) shown below. Test the magazine s belief that the mean nicotine content is greater than 40 mg at a 0.01 significance level, making use of the output from SPSS below. 47.3, 39.3, 40.3, 38.3, 46.3, 43.3, 42.3, 49.3, 40.3, 46.3 One-Sample Statistics N Mean Std. Deviation Std. Error Mean Nicotine One-Sample Test Test Value = 40 95% Confidence Interval of the Difference t df Sig. (2-tailed) Mean Difference Lower Upper Nicotine

9 Section 9-2 Inferences about Two Proportions Example: In a study of women and coronary heart disease, the following sample results were obtained: Among 10,239 women with a low level of physical activity (less than 200 kcal/wk), there were 101 cases of coronary heart disease. Among 9877 women with physical activity measured between 200 and 600 kcal/wk, there were 56 cases of coronary heart disease (based on data from a paper published in Journal of the American Medical Association). Use a 0.05 significance level to test the claim that the rate of coronary heart disease is higher for women with the lower levels of physical activity. What does the conclusion suggest? 9

10 The New York Times ran an article about a study in which Professor Denise Korniewicz and other John Hopkins researchers subjected laboratory gloves to stress. Among 240 vinyl gloves, 63% leaked viruses. Among 240 latex gloves, 7% leaked viruses. At the significance level, test the claim that vinyl gloves have a higher rate of virus leak than latex gloves. 10

11 The Joint Commission on Accreditation of Healthcare Organizations mandated that hospitals ban smoking by In a study of the effects on this ban, subjects who smoke were randomly selected from two populations. Among 843 smoking employees of hospitals with the smoking ban, 56 quit smoking one year after the ban. Among 703 smoking employees from work places without a smoking ban, 27 quit smoking a year after the ban (based on data from a paper published in Journal of the American Medical Association). Is there a significant difference between the two proportions at a 0.05 significance level? Does it appear that the ban had an effect on the smoking quit rate? How about at a 0.01 significance level? 11

12 Section 9-3 Inferences about Two Means: Independent Samples Example: The following data, from Federal Trade Commission, give the measured nicotine contents of randomly selected filtered and non-filtered king-size cigarettes. All measurements are in milligrams. Use a 0.05 significance level to test the claim that king-size cigarettes with filters have a lower mean amount of nicotine than non-filtered king-size cigarettes. Filtered kings Nonfiltered kings n 1 21 n 2 8 x x s s

13 In an experiment designed to test the effectiveness of paroxetine for treating bipolar depression, subjects were measured using the Hamilton depression scale with the results given below (based on data from an article in American Journal of Psychiatry). Use a 0.05 significance level to test the claim that the treatment group and the placebo group come from populations with the same mean. What does the hypothesis test suggest about paroxetine as a treatment for bipolar depression? Placebo group: n 43 x s = 3.87 Paroxetine treatment group: n 33 x s =

14 Use the output from SPSS below, based on Data Set 20 in Appendix B, to test the claim that the mean weight of pre-1964 silver quarters is equal to the mean weight of post-1964 quarters at a 0.01 significance level. Group Statistics Type N Mean Std. Deviation Std. Error Mean Weight (grams) Pre-1964 Quarters Post-1964 Quarters Independent Samples Test Weight (grams) t-test for Equality of Means Mean Std. Error 95% Confidence Interval of the Difference t df Sig. (2-tailed) Difference Difference Lower Upper Equal variances assumed Equal variances not assumed