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H OW MANY DAYS UNTIL THANKSGIVING Slide

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U PCOMING IN C LASS Quiz #6 this Wednesday HW #12 due Sunday Exam #2 next Wednesday Data Project Due by 5pm Thursday December 5 th via or my department mailbox.

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C HAPTER 20 Comparing Means

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C OMPARING T WO M EANS Comparing two means is not very different from comparing two proportions. This time the parameter of interest is the difference between the two means, 1 – 2. Examples, Height of black vs. height of whites SAT scores of men vs SAT scores of women Sugar content in Children’s cereal vs. Sugar content in Adult’s cereal

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When the conditions are met, we are ready to find the confidence interval for the difference between means of two independent groups. The confidence interval is where the standard error of the difference of the means is The critical value depends on the particular confidence level, C, that you specify and on the number of degrees of freedom, which we get from the sample sizes and a special formula. T WO -S AMPLE T -I NTERVAL Slide 1- 5

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D EGREES OF F REEDOM The special formula for the degrees of freedom for our t critical value is a bear: Because of this, we will let technology calculate degrees of freedom for us! Slide 1- 6

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R OUTE T O S CHOOL A student takes two routes to class. Route A and Route B. Each day she randomly selects a route until she has walked each route 20 times. Route A Mean = 44 St.D.= 5 Route B Mean =47 St. D. 4 Create a 95% confidence interval for the difference between the routes, and interpret it. Slide 1- 7

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W E ARE 95% CONFIDENT THE TRUE DIFFERENCE BETWEEN R OUTE A AND R OUTE B IS IN THE INTERVAL (0.09, 5.91). W HICH ROUTE IS FASTER ? 1. Route A 2. Route B 3. Our data shows no difference. Slide 1- 8

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T ESTING THE D IFFERENCE B ETWEEN T WO M EANS Slide 1- 9 We test the hypothesis H 0 : 1 – 2 = 0, where the hypothesized difference, 0, is almost always 0, using the statistic The standard error is When the conditions are met and the null hypothesis is true, this statistic can be closely modeled by a Student’s t -model with a number of degrees of freedom given by a special formula. We use that model to obtain a P-value.

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C OMPARING DIFFERENT TEACHING METHODS Slide 1- 10

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Slide 1- 11

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I S THE NEW METHOD BETTER THAN THE TRADITIONAL METHOD ? W HAT IS THE APPROPRIATE HYPOTHESIS TEST ? 1. Ho: μ1-μ2=0 Ha: μ1-μ2≠0 2. Ho: μ1-μ2=0 Ha: μ1-μ2>0 3. Ho: μ1-μ2=0 Ha: μ1-μ2<0 Slide 1- 12

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W HAT IS YOUR CONCLUSION BASED ON THE DATA ? 1. Reject null. There is sufficient evidence that the new activities are better 2. Reject null. There is NOT sufficient evidence. 3. Fail to reject null. There is NOT sufficient evidence. 4. Fail to reject null. There is sufficient evidence that the new activities are better. Slide 1- 13

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F IND THE P- VALUE AND COMPARE YOUR TEST RESULTS ml homework.com/statistics_tables/statistics_tables. html Calculators ocuments/ComparingMeans_001.pdf Slide 1- 14

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C OMPARING SPORTS LEAGUES Slide 1- 15

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I NTERPRET YOUR INTERVAL. W E ARE 90% CONFIDENT THAT … 1. the points scored per game in both leagues will fall in the interval 2. the amount by which the points scored in League 2 games exceed the points scored in League 1 games will fall in the interval 3. the amount by which the points scored in League 1 games exceed the points scored in League 2 games will fall in the interval Slide 1- 16

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D OES THE INTERVAL SUGGEST THAT THE TWO LEAGUES DIFFER IN AVERAGE NUMBER OF POINTS SCORED PER GAME ? 1. No, because the interval does not contain zero 2. Yes, because the interval contains zero 3. No, because the interval contains zero 4. Yes, because the interval does not contain zero Slide 1- 17

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C OMPARING TV P ROGRAMS Slide 1- 18

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W HAT IS THE BEST CONCLUSION ? T EST USING A 95% CI. 1. Viewer’s memory are different, since we reject the null 2. Viewer’s memory are not different, since we reject the null 3. Viewer’s memory are different, since we do not reject the null 4. Viewer’s memory are not different, since we do not reject the null Slide 1- 19

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B ASED ON OUR DATA AND CI, WHAT COULD YOU SAY ABOUT THE TWO PROGRAMS. 1. Program A helps viewers remember commercials better than Program B. 2. Program B helps viewers remember commercials better than Program A. 3. There is no statistical difference between Program A and Program B. Viewers remember the commercials just the same. Slide 1- 20

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R UNNER ’ S P ROBLEM In a certain running event, preliminary heats are determined by random draw, so it would be expected that the abilities of runners in the various heats are about the same, on average. There are 7 runners in each race, but due to an outlier in heat 2, we only have 6 observations for heat 2. Slide 1- 21

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R UNNER ’ S P ROBLEM The statistics for heats 2 and 5 are below. Heat 2 Mean: seconds SD: N=6 Heat 5 Mean: seconds SD: N=7 Slide 1- 22

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I S THERE ANY EVIDENCE THAT THE MEAN TIME TO FINISH IS DIFFERENT FOR THE HEATS ? W HAT IS THE APPROPRIATE HYPOTHESIS TEST ? Slide Ho: μ2-μ5=0 Ha: μ2-μ5≠0 2. Ho: μ2-μ5=0 Ha: μ2-μ5>0 3. Ho: μ2-μ5=0 Ha: μ2-μ5<0

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D ETERMINE THE TEST STATISTICS Slide

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A T THE 0.05 SIGNIFICANCE LEVEL, TEST THE HYPOTHESIS THAT THE HEATS HAVE DIFFERENT AVERAGE TIMES. Slide Do reject the null hypothesis. There is not sufficient evidence to support the claim that the mean running times in heat 2 and 5 are different. 2. Do reject the null hypothesis. There is sufficient evidence to support the claim that the mean running times in heat 2 and 5 are different. 3. Do not reject the null hypothesis. There is not sufficient evidence to support the claim that the mean running times in heat 2 and 5 are different. 4. Do not reject the null hypothesis. There is sufficient evidence to support the claim that the mean running times in heat 2 and 5 are different.

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U PCOMING IN C LASS Quiz #6 this Wednesday HW #12 due Sunday Exam #2 next Wednesday Data Project Due by 5pm Thursday December 5 th via or my department mailbox.

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