HOW MANY DAYS UNTIL THANKSGIVING

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1. 152. 163. 174. 185. 196. 20

UPCOMING IN CLASS

Quiz #6 this Wednesday

HW #12 due Sunday

Exam #2 next Wednesday

Data Project Due by 5pm Thursday December 5th via email or my department mailbox.

CHAPTER 20Comparing Means

COMPARING TWO MEANS 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

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.

TWO-SAMPLE T-INTERVAL

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DEGREES OF FREEDOM

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!

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ROUTE TO SCHOOL 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.

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WE ARE 95% CONFIDENT THE TRUE DIFFERENCE BETWEEN ROUTE A AND ROUTE B IS IN THE INTERVAL (0.09, 5.91). WHICH ROUTE IS FASTER?1. Route A2. Route B3. Our data shows no

difference.

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TESTING THE DIFFERENCE BETWEEN TWO MEANS

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SE y y

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We test the hypothesis H0:1 – 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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COMPARING DIFFERENT TEACHING METHODS

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IS THE NEW METHOD BETTER THAN THE TRADITIONAL METHOD? WHAT 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

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WHAT 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.

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FIND THE P-VALUE AND COMPARE YOUR TEST RESULTS

http://www.stat.tamu.edu/~west/applets/tdemo.html

http://www.tutor-homework.com/statistics_tables/statistics_tables.html

Calculators http://economics.illinoisstate.edu/aohler/eco1

38/documents/ComparingMeans_001.pdf

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COMPARING SPORTS LEAGUES

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INTERPRET YOUR INTERVAL. WE 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

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DOES THE INTERVAL SUGGEST THAT THE TWO LEAGUES DIFFER IN AVERAGE NUMBER OF POINTS SCORED PER GAME?1. No, because the interval

does not contain zero2. Yes, because the

interval contains zero3. No, because the interval

contains zero4. Yes, because the

interval does not contain zero

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COMPARING TV PROGRAMS

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WHAT IS THE BEST CONCLUSION? TEST 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

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BASED 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.

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RUNNER’S PROBLEM

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.

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RUNNER’S PROBLEM

The statistics for heats 2 and 5 are below. Heat 2

Mean: 52.135 seconds SD: 0.635 N=6

Heat 5 Mean: 52.333 seconds SD: 0.961 N=7

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IS THERE ANY EVIDENCE THAT THE MEAN TIME TO FINISH IS DIFFERENT FOR THE HEATS? WHAT IS THE APPROPRIATE HYPOTHESIS TEST?

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1. Ho: μ2-μ5=0 Ha: μ2-μ5≠02. Ho: μ2-μ5=0 Ha: μ2-μ5>03. Ho: μ2-μ5=0 Ha: μ2-μ5<0

DETERMINE THE TEST STATISTICS

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1. -0.1982. 0.4353. -0.454. 0.662

AT THE 0.05 SIGNIFICANCE LEVEL, TEST THE HYPOTHESIS THAT THE HEATS HAVE DIFFERENT AVERAGE TIMES.

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1. 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.

UPCOMING IN CLASS

Quiz #6 this Wednesday

HW #12 due Sunday

Exam #2 next Wednesday

Data Project Due by 5pm Thursday December 5th via email or my department mailbox.