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Fall 2010 Math 227 Test #3 Name: ___________________ For confidence interval, please write down the critical value(s) and margin of error (if needed), then write the confidence interval. For Hypothesis testing, use either the traditional method or the P-value method. 1. (7) The department of Mathematics at a four-year university wants to estimate the average age of students who apply to their graduate program with 98% confidence level. If the standard deviation of the ages is known to be 10 years of age with a margin of error of 2 years, how large must the sample be? 2. (12) According to Crime in the United States, a publication of the FBI, the mean value lost to purse snatching was $356 in 2008. For last year, 12 randomly selected purse-snatching offenses yielded the following values lost, to the nearest dollar. At the 5% significance level, test the claim that the mean value lost to purse snatching has decreased from the 2008 mean. Assume the population has normal distribution. 231 446 296 386 189 293 261 250 229 372 290 454 1 3. The U.S. National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals. Independent random samples of 39 male patients and 35 female patients gave the following data on the length of stay, in days. Construct a 90% confidence interval for the difference between the two means. Can you conclude that, on average, the lengths of stay in short-term hospitals by males and females differ? Male: 4 4 12 18 9 6 12 10 3 6 15 7 3 13 1 2 10 13 5 7 1 23 9 2 1 17 2 24 11 14 6 2 1 8 1 3 19 3 1 (15) Female: 14 4 4 4. 7 4 9 15 3 10 1 5 7 12 18 3 1 12 6 3 5 5 7 1 9 21 7 6 4 7 2 1 2 14 5 15 A Statistics major attending UCLA wants to take a survey of families who like Math. He wants to be 96% sure that the true proportion of families who like Math is no more than 1.5% of the true proportion. Compute the sample size if she has some idea of past research about the estimate of this proportion and that is 25%. (7) 2 5. (15) In one trip of the Royal Caribbean cruise ship Freedom of the Seas, 338 of the 3823 passengers become ill with a Norovirus. AT about the same time, 276 of the 1652 passengers on the Queen Elizabeth II cruise ship became ill with a Norovirus. Treat the sample results as a simple random sample from large populations, and use a 0.01 significance level to test the claim that the rate of Norovirus illness on the Freedom of the Seas is less than the rate on the Queen Elizabeth II. 6. (10) In a poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all incomes on tax returns. Construct a 95% confidence interval estimate of the percentage of all adults who have that belief. 3 7. (12)A simple random sample of 32 cars yields a mean weight of 3605.3 lbs, a standard deviation of 501.7 lbs., and the sample weight appear to be from a normal distributed population. Use a 0.01 significance level to test the claim that the standard deviation of the weights of cars is less than 520 lbs. 8. (10) Listed below are weights (in pounds) of glass discarded in one week by randomly selected households. The sample weights come from a normal distributed population. 3.52 8.87 3.99 3.64 2.33 3.21 0.25 4.94 a. What is the best point estimate of the weight of glass discarded by all households in one week? b. Construct a 95% confidence interval estimate of the mean weight of glass discarded by all households. 4 9. Listed below are ten voltage levels recorded in Melanie’s home on ten different days. These values come from a normally distributed population. Use the sample data to construct a 95% confidence interval estimate of the standard deviation of all voltage level. 123.3 123.5 123.7 123.4 123.6 123.5 123.5 123.4 123.6 123.8 (10) 10. (6) Find the critical values. a. Assume that the normal distribution applies. Find the critical values. Right-tailed test; 0.01 . b. Assume that t-distribution applies. Find the critical values. Right-tailed test; 0.01 , and n = 23. c. Assume that the chi-square distribution applies. Find the critical values. Right-tailed test; 0.01 , n = 23. 5