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How many colleges did you apply to?. Type the number into your clicker and hit send. 10-2 Estimating a Population Mean ( Unknown). Confidence Intervals in the Calculator. - PowerPoint PPT Presentation

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How many colleges did you apply to?Type the number into your clicker and hit send

10-2Estimating a Population Mean( Unknown)2Confidence Intervals in the CalculatorHigh School students who take the SAT Mathematics exam a second time generally score higher than on their first try. The change in the score has a Normal distribution with standard deviation =50. A random sample of 250 students gain on average x-bar=22 points on their second try.

Construct a 95% Confidence interval for

Confidence Intervals Involving ZUsing the Calculator

7

Standard error: You are estimating the standard deviationbut there will likely be some error involved because we are estimating it from sample data.

In other words the standard error is (most likely) an inaccurate estimate of a (population) standard deviation.9The t distributions

10The t-statistic was introduced in 1908 by William Sealy Gosset, a chemist working for the Guinness brewery in Dublin, Ireland ("Student" was his pen name). Gosset devised the t-test as a way to cheaply monitor the quality of stout. The t distributionsThere is a different t-distribution for each sample size n.We specify a t distribution by giving its degrees of freedom, which is equal to n-1We will write the t distribution with k degrees of freedom as t(k) for short.We also will refer to the standard Normal distribution as the z-distribution.12Comparing t and z distributions

Compare the shape, center, and spread of the t-distribution with the z-distribution.As the degrees of freedom k increase, (the sample size increases), the t-distribution is increasingly Normal. 13

Our formula is the same as it was for z-intervals EXCEPT we replace sigma with s!!!

14Finding t with Table CSuppose you want to construct a 95% confidence interval for the mean of a population based on a SRS of size n=12. What critical value t should you use?

15Finding t with Table CSuppose you want to construct a 95% confidence interval for the mean of a population based on a SRS of size n=12. What critical value t should you use?

16Finding t with Table CSuppose you want to construct a 90% confidence interval for the mean of a population based on a SRS of size n=15. What critical value t should you use?

17Finding t with Table CSuppose you want to construct a 99% confidence interval for the mean of a population based on a SRS of size n=34. What critical value t should you use?

18Suppose you want to construct a 80% confidence interval for the mean of a population based on a SRS of size n=95. What critical value t should you use?a) 1.290b) .846c) 1.292c) .845

1)SRS2) Normality- n < 15 : Use t procedures if data are close to Normal with no outliers- n 15 : Use t procedures except in cases of outliers of strong skew- n 30 : Use t-procedures even for clearly skewed distributions (cannot have extreme outliers)3) Independence

20Lets use our class data to construct a 95% confidence interval for the true mean number of colleges that high school seniors applied to in 2013.

21One sample t interval for muStep 1: STATEStep 2: PLANStep 3: CALCULATIONS

Step 4: INTERPERATION22State: We are estimating ________, the true mean ______________________________________________________________. Plan:Procedure:Conditions: 1)2)

3)

Calculations:

Interpretation: We are 95% confident that the true mean

Last year, 750,000 applicants submitted 3 million applications, an average of four per student College Decision Day: More Applications, More Problems|TIME.comhttp://nation.time.com/2013/05/01/as-college-applications-rise-so-does-indecision/#ixzz2sr0ANbp4Which of the following changes will make a t-distribution more Normal?Paired t-proceduresTo compare the responses of the two treatments in a matched pairs design or before and after measurements on the same subjects, apply the one sample t procedures to the differences observed between the pairs. = the mean difference between each pair Ex) Mrs. Skaff gave a new study tool to her students to see if it would improve their test scores. She matched students based on current grade and randomly gave one student in each pair the study tool.

Paired t-procedures = the mean difference between each pair Ex) Mrs. Skaff gave a new study tool to her students to see if it would improve their test scores. She matched students based on current grade and randomly gave one student in each pair the study tool. She wants to know if the study tool improved test scores.

927381899590967285889073848488919370808820-357-13250Given Study Tool

No Study Tool

Study No StudyConfidence Intervals in the Calculator

You still need all other steps!!!!Ronald McDonalds sister Diana Rhea is the purchasing manager for domestic hamburger outlets. The company has decided to provide a free package of Tums to any complaining customer. In order to estimate monthly demand, she took a sample of 5 outlets and found the number of Tums distributed to customers in a month was250, 280, 220, 280, 320Find the sample mean and sample standard deviationConstruct a 90% confidence interval on the average monthly demand per outlet.

30Homework!

ExpressPoll 2/11/2014 10:08:36 AM

ExpressPoll 2/11/2014 10:14:18 AM

ExpressPoll 2/11/2014 10:22:39 AM

ExpressPoll 2/11/2014 10:43:23 AM

ExpressPoll 2/11/2014 11:15:05 AM