Unformatted text preview: Department of Mathematics Name: ________________________________ Poly ID: _______________________________ Instructor's Name: _______________________ Course No:_____________________________ Course Section: _________________________ Homework Section No: ___________________ Willis Thai 6.41 MA2222 { yielded Y ' HW03 . Find a A random sample of size 16 from the normal distribution W{ 95% confidence interval for . . 6.410 During the Friday night shift, mints were selected at random from a production line and weighed. They had an average weight of Y grams and grams. Give the lower endpoint of a 90% onesided confidence interval for , the mean weight of all the mints. { . { 3 { { 3 3 { % . { % {& 3
' 3 %  { % {& 6.412 A leakage test was conducted to determine the effectiveness of a seal designed to keep the inside of a plug air tight. An air needle was inserted in the plug and this was placed under water. The pressure was then increased until leakage was observed. Let equal the pressure in pounds per square inch. Assume that the distribution of is W{ {. Using the following observations of , 3.1 3.3 4.5 2.8 3.5 3.5 3.7 4.2 3.9 3.3 (a) Find a point estimate of . % (b) Find a point estimate of .
# { 3 . " %# $ 3 { 3 { J$ { (c) Find a 95% onesided confidence interval for % 3 { 3 # (#{ . {$ 3 3 % % that provides an upper bound for .
" '#$ #" { 3 3 % { 6.415 Students took samples of water from the east basin of Lake Macatawa and measured the amount of sodium in parts per million. For their data they calculated Y and . Find an approximate 90% confidence interval for , the mean of the amount of sodium parts per million. . 6.51 The length of life of brand light bulds is assumed to be W{ {. The length of life of { and independent of that of . If a random brand light bulbs is assumed to be W{ sample of brand light bulbs yielded a mean of Y hours and a random sample of size brand light bulbs yielded a mean of Y hours, find a 90% confidence interval for . . { 3 % { 3 {  3 3 % { . & && %' 3 3  & && %' Willis Thai . . MA2222 HW03 6.53 means of the populations of heights. Assume that . . {. %
{ #{ $ { #{ $ # Independent random samples of the heights of adult males living in two countries yielded the following results: ,Y inches, Y inches and ,Y inches, inches. Find an approximate 98% confidence interval for the difference Y . Y of the Y # #&0 $' {. % % .  . %%% % . . { ' &  $ ' % . %%% %  ' &  $ ' . % . % { % ##0# $'  .  { Y #{ # #  #' #$ . %  $ { Y. #{ $ # %  # ##0# $'  #&0 $' # #  #' #$ 6.61 Let equal the length (in centimeters) of a certain species of fish when caught in the spring. A random sample of observations of is (a) Give a point estimate of the standard deviation J (b) Find a 95% confidence interval for . From Table X: I { % { J
{ #{ J$ # # (#{ . {$
{ of this species of fish. 3 3J %% , I {: #{ % $# $ % 3 3 $# $ % 6.62 A random sample of assumed to be W{ wheels of cheese yielded the following weights in pounds, (a) Give a point estimate of . J$ J % % (b) Find a 95% confidence interval for . From Table X: I J
{ #{ # # (#{ . {$
{ 3 3J ,I #{ ' $'' % 3 3 ' $'' Willis Thai MA2222 HW03 { { (c) Find a 90% confidence interval for . From Table X: I { %% { 6.64 J
{ #{ 3 3J %%, I { #{ % ' $'' 3 3 ' $'' For the data in Exercise 6.49: Find a 95% confidence interval for (a) .  {J . {J $
$ (b) . ? (c) {J . { {J . {J $
$ # From Table X: I { { J % C { % % having minimum length.
{ #{  {J . { @ 0 { % 0 % D { % % { 3 3J { ,I #{ # #' % 3 3 # #' ...
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 Fall '07
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 Statistics, Normal Distribution, Standard Deviation, Willis Thai

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