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## Introduction to Mathematical Statistics

by: Mrs. Triston Collier

34

0

1

# Introduction to Mathematical Statistics STAT 312

Marketplace > University of Wisconsin - Madison > Statistics > STAT 312 > Introduction to Mathematical Statistics
Mrs. Triston Collier
UW
GPA 3.57

Staff

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COURSE
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Staff
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1
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KARMA
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## Popular in Statistics

This 1 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 312 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 34 views. For similar materials see /class/205088/stat-312-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.

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Date Created: 09/17/15
Stat 312 Fall 2003 10092003 Discussion 6 MidTerm Review Sections Thursday October 23 2003 in discussion sections The OneSample t Test Ha Rejection Region for a Level 1 Test gt 0 t 2 75047171 lt 0 75S itamil i 0 752 to 2771 0F 75 S i750 2771 Example 1 The temperature of each of 9 samples of a certain machine was determined The sample average is 212l23 F Assume the distribution of the temperature is normal a Suppose a is unknown and the sample standard deviation is 1154 Test H0 M 205 versus Ha M f 205 using a two tailed level 05 test b Suppose a SJ Test H0 M 205 versus Ha M gt 205 using a onetailed level 05 test B and Sample Size Determination The sample size n for which a level a test also has 5M B at the alternative value M is 2 M for a onetailed test Ho i 2 W for a twotailed test Example 2 Consider a twotailed level 05 test and a SJ Using the information in Example 1 a What is the probability of type ll error when M 210 6210 b What is the minimal sample size required to ensure that 5210 1 when a 05 Example 31Exercise 61 and 62 page 356 Devore 6th a A sample of 50 lenses used in eyeglasses yields a sample mean thickness of 305 mm and a sample standard deviation of 34 mmi The desired true average thickness of such lenses is 320 mm Does the data strongly suggest that the true average thickness of such lenses is something other than what is desired Test using a 05 b Suppose the experimenter had believed before collecting the data that the value of a was approximately 30 If the experimenter wished the probability of a type ll error to be 05 when M 300 was a samp e size 50 unnecessarily large Example 4 Exercise 66 page 356 Devore 6th The article 77Orchard Floor Management Utilizing SoilApplied Coal Dust for Frost Protection77 Agri and Forest Meteorology 1988 7182 reports the following values for soil heat ux of eight plots covered with coal dusti 34 354 34 37 325 289 184 249 The mean soil heat ux for plots covered only with grass is 290 Assuming that the heat ux distribution is approximately normal does the data suggest that the coal dust is effective in increasing the mean heat ux over that for grass Test the appropriate hypothesis using a i05i TingLi Lin

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