Unformatted text preview: Department of Mathematics Name: ________________________________ Poly ID: _______________________________ Instructor's Name: _______________________ Course No:_____________________________ Course Section: _________________________ Homework Section No: ___________________ Willis Thai 8.21 MA2222 HW05 Assume that IQ scores for a certain population are approximately W{ {. To test against the onesided alternative hypothesis 2 , we take a random sample of size from this population and observe Y . Do we accept or reject at the (a) 5% significance level? F { { F { J Since is not in the critical interval, we accept H" . (b) 10% significance level?
" "  { { Since 8.23 { J (b) A random sample of 2
" Let equal the Brinell hardness measurement of ductile iron subcritically annealed. Assume that the distribution of is W{ {. We shall test the null hypothesis against the alternative hypothesis 2 using observations of . (a) Define the test statistic and a critical region that has a significance level of . Sketch a figure showing this critical region. . I. " J F { % { F { J is in the critical interval, we reject H" . observations of { % yielded the following measurements 8.210 A company that manufactures brackets for an auto maker regularly selects brackets from the production line and performs a torque test. The goal is for the mean torque to equal 125. Let equal the torque and assume that is W{ {. We shall use a sample of size to against a twosided alternative hypothesis. test (a) Give the test statistic and a critical region with significance level . Sketch a figure illustrating the critical region. I. " { 4 {J . { " "$' { J $ J (b) Use the following observations to calculate the value of the test statistic and state your conclusion. Calculate the value of the test statistic and clearly give your conclusion. and is not in the critical interval, so we accept H" . Willis Thai MA2222 HW05 , J$ #$ %% % , J
# #! #$' % % , which is not in the critical interval, so we accept H" . 8.211 Let equal the number of pounds of butterfat produced by a Holstein cow during the 305day milking period following the birth of a calf. We shall test the null hypothesis against the alternative hypothesis 2 . (a) Give the test statistic and a critical region that has a significance level of , assuming that there are observations. $ {J . {J $ $ { { 3 $ {J . { " "' $ J 2
$ % J. (b) Calculate the value of the test statistic and give your conclusion using the following observations of .
$ {J . { " $ " { { $ 8.216 Let be a random sample of size from the normal distribution W{ against (a) Find a critical region, C, of size for testing $ {J . {J $ $ 4 $ {J . { " "' % % $
" (c) Find a 98% onesided confidence interval that gives an upper bound for . J$ % % , which is not in the critical interval, so we accept H" . . {. (b) Find the approximate value of , the probability of Type II error, for the critical region C of part (a). % $ { $3 % { 3 % % $ % " " { %{ . ...
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 Fall '07
 Yang
 Math, Statistics, Null hypothesis, Statistical hypothesis testing, Department of Mathematics, critical region, Willis Thai

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