Unformatted text preview: Department of Mathematics Name: ________________________________ Poly ID: _______________________________ Instructor's Name: _______________________ Course No:_____________________________ Course Section: _________________________ Homework Section No: ___________________ Willis Thai 6.81 MA2222 HW04 Let equal the tarsus length for a male grackle. Assume that the distribution of X is W{ {. Find the sample size that is needed so that we are 95% confident that the maximum error of the estimate of is 0.4. J $ { % {$ 6.83 A company packages powdered soap in "6pound" boxes. The sample mean and standard deviation of the soap in these boxes are currently 6.09 and 0.02 pounds. If the mean fill can be lowered by 0.01 pounds, $14,000 would be saved per year. Adjustments were made in the filling equipment, but it can be assumed that the standard deviation remains unchanged. (a) How large a sample is needed so that the maximum error of the estimate of the new is with 90% confidence? { { (b) A random sample of size confidence interval for . J $ { % {$ { {$ {$ {$ F { %{ % (c) Estimate the savings per year with these new adjustments. %. % { F{ %% / %/{ { yielded Y % % and . Calculate a 90% (d) Estimate the proportion of boxes that will now weigh less than 6 pounds. 6.86 A light bulb manufacturer sells a light bulb that has a mean life of 1450 hours with a standard deviation of 33.7 hours. A new manufacturing process is being tested and there is interest in knowing the mean life of the new bulbs. How large a sample is required so that Y / is a 95% confidence interval for ? You may assume that the change in the standard deviation is minimal. J $ { % {$ { $ {$ 6.87 For a public opinion poll for a close presidential election, let denote the proportion of voters who favor candidate A. How large a sample should be taken if we want the maximum error of the estimate of to be equal to (a) 0.03 with 95% confidence? { {$ (b) 0.02 with 95% confidence? J $ { % {$ % Willis Thai J { {$ (c) 0.03 with 90% confidence? J $ $ MA2222 { % {$ { HW04 {$ 6.814 Let equal the proportion of New York City residents who feel that the quality of life in New York City has become worst in the past few years. To update the estimate given in Exercise 6.79, how large a sample is required to be 98% confident that the maximum error of the estimate of is 0.025? $ { %%{{ . %%{ { {$ %% %% J $ { { 8.13 against : Let be { {. To test : if and only if 3 . (a) Determine the significance level of the test. Using Poisson: %0 % {I 3 { (b) Find the probability of the Type II error if in fact 0 . . W{ 3 { . Let , we reject and accept 6.812 A seed distributor claims that 80% of its beet seeds will germinate. How many seeds must be tested for germination in order to estimate , the true proportion that will germinate, so that the maximum error of the estimate is with 90% confidence? $ { %{{ { J { {$ % % { {$ { {$ . 8.14 8.18 It was claimed that 75% of all dentists recommended a certain brand of gum for their gumchewing patients. A consumer group doubted this claim and decided to test : , where is the proportion of dentists who against the alternative hypothesis : recommended this brand of gum. A survey of 390 dentists found that 273 recommended this brand of gum. Which hypothesis would you accept if the significance level is denote the probability that, for a particular, tennis player, the first serve is good. Since , this player decided to take lessons in order to increase . When the lessons are completed, the hypothesis : will be tested against : 2 based on trials. Let Y equal the number of first serves that are good, and let the critical region be defined by V {Y Y 4 {. (a) Determine W{ 4 {. Use Table II in the Appendix. {I 4 { . {I 3 { . % % (b) Find W{ { when ; that is, W{ 3 {. Use Table II. {I 3 { {I 4 { . {I 3 { . % % Willis Thai (a) I ? MA2222 HW04 . % 2. Reject (b) ? . % 2. Accept I " { !{{ # " { !{{ # " ' { . % ,. " "' . " ' { . % ,. " "# . 8.110 Let equal the proportion of drivers who use a seat belt in a state that does not have a mandatory seat belt law. It was claimed that . An advertising campaign was conducted to increase this proportion. Two months after the campaign, Y out of a random sample of drivers were wearing their seat belts. Was the campaign successful? (a) Define the null and alternative hypotheses. H" J H# J 2 (b) Define a critical region with a significance level. J"  #"& ' " { { (c) What is your conclusion?  J" { . J" { J { % { %   is located in the critical region, so the campaign was successful. 8.115 According to a population census in 1986, the percentage of males who are 18 or 19 years old that are married was 3.7%. We shall test whether this percentage increased from 1986 to 1988. (a) Define the null and alternative hypotheses. H" J H# J 2 (b) Define a critical region that has an approximate significance level of . Sketch a standard normal pdf to illustrate this critical region. J" (c) if Y J" { . J" { J  @  out of a random sample of J % F males, each 18 or 19 years old, were married Willis Thai MA2222 HW04 $" %"" (U.S. Bureau of the Census, Statistical Abstract of the United States: 1988), what is your conclusion? Show the calculated value of the test statistic on your figure in part (b). 2 , so the percentage increased. ...
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 Fall '07
 Yang
 Math, Statistics, Normal Distribution, Statistical hypothesis testing, maximum error, Willis Thai

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