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1. An estimator is called consistent if its variance and standard deviations consistently remain the same regardless of changes in the sample size. True False 2. When determining the sample size n, if the value found for n is 79.2, we would choose to sample 79 observations. True False 3. The larger the p-value, the more the chance of rejecting the null hypothesis. True False 4. A fastener manufacturing company uses a chi-square goodness of fit test to determine if a population of all lengths of ¼ inch bolts it manufactures is distributed according to a normal distribution. If we reject the null hypothesis, it is reasonable to assume that the population distribution is at least approximately normally distributed. True False 5. The chi-square distribution is a continuous probability distribution that is skewed to the left. True False 6. The error term in the regression model describes the effects of all factors other than the independent variables on y (response variable). True False 7. When constructing a confidence interval for a sample proportion, the t distribution is always appropriate if the sample size is small. True False 8. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n=100 will be narrower than a confidence interval for a population mean based on a sample of n=50. True False 9. The sampling distribution of the sample mean is always normally distributed according to the Central Limit Theorem. True False 10. The error term is the difference between the observed value of the dependent variable and the predicted value of the dependent variable. True False 11. We do not need to perform the continuity correction if the population is 20 times or more than the sample size. True False 12. For a continuous distribution, Probability of (X greater than or equal to 10) is less than the probability of (X greater 10) True False 13. In a regression model the population of potential error terms is assumed to have a t-distribution. True False 14. The least squares simple linear regression line minimizes the sum squares of the vertical deviations between the line and the data points. (Points : 8) True False 15. In testing the difference between two means from two independent populations, the sample sizes do not have to be equal to be able to use the Z statistic. True False 16. To investigate the rate at which employees with cancer are fired or laid off, a telephone survey was taken of 100 cancer survivors who worked while undergoing treatment. Seven (7) were either fired or laid off due to their illness. Construct a 90% confidence interval for the true percentage of all cancer patients who are fired or laid off due to their illness. [0.0000 0.2034] [0.0371 0.1029] [0.0039 0.1361] [0.0078 0.1400] [0.0278 0.1122] 17. The area under the normal curve between z=2 and z=3 is ________________ the area under the normal curve between z=1 and z=2. Greater than Less than Equal to Answers 1, 2, or 3 depending on the value of the Mean Answers 1, 2, or 3 depending on the value of the Standard Deviation 18. For a given multiple regression model with three independent variables, the value of the adjusted multiple coefficient of determination is _________ less than R . Always Sometimes Never Can be greater or less depending on the standard error 19. A new company is in the process of evaluating its customer service. The company offers two types of sales: 1. Internet sales; 2. Store sales. The marketing research manager believes that the Internet sales are more than 10% higher than store sales. The null hypothesis would be: Pinternet-Pstore>.10 Pinternet-Pstore<.10 Pinternet-Pstore >=.10 Pinternet-Pstore <=.10 Pinternet-Pstore=.10 20. If a population distribution is known to be normal, then it follows that: The sample Mean must equal the population mean The sample Mean is skewed for small samples but becomes more and more normal as sample size increases The sample Standard Deviation must equal the population standard deviation The Sample Proportion must equal the population Proportion None of the above 21. One survey conducted by a major leasing company determined that the Lexus is the favorite luxury car for 25% of leases in Atlanta. Suppose a US car manufacturer conducts its own survey in an effort to determine if this figure is correct. Of the 384 leases in Atlanta surveyed, 79 lease a Lexus. Calculate the appropriate test statistic to test the hypotheses. -2.15 -2.00 (Some would also consider -2.00 as a second correct value) -0.91 2.00 2.51 22. The Ohio Department of Agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level. For premium grade, 14 out of 105 samples failed (they didn't meet ASTM specification and the FTC Octane posting rule). How many samples would be needed to create a 99% confidence interval that is within 0.02 of the true proportion of premium grade fuel-quality failures? (14/105)(91/105)(2.5758/0.02)2 = 4148 2838 1913 744 54 23. A state education agency designs and administers high school proficiency exams. Historically, time to complete the exam was an average of two hours with a standard deviation of 5 minutes. Recently the format of the exam changed and the claim has been made that the time to complete the exam has changed. A sample of 50 new exam times yielded an average time of 118 minutes. Calculate a 99% confidence interval based on the sample result. Confidence Interval = ( 118 - 2.576(5.000)/sqrt(50) , 118 + 2.576(5.000)/sqrt(50) ) = ( 116.18 , 119.82 ) [117.61 120.09] [117.36 119.39] [116.18 119.82] [115.67 120.33] [115.82 120.18] 24. The MPG (Miles per Gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What is the probability that the MPG for a selected mid-size car would be: More than 33.2? 100P(MPG>33.2) = 100P(Z > (33.2-32)/0.8) = 43.32% 6.68% 93.32% 86.64% 13.36% 25. If we are testing the significance of the independent variable X1 in Regression and we reject the null hypothesis H0: B1=0, we conclude that: X is significantly related to Y (should be X1 not X) X1 is not significantly related to Y X1 is an unimportant independent variable B1 is significantly related to the dependent variable Y 26. In a manufacturing process, we are interested in measuring the average length of a certain type of bolt. Based on a preliminary sample of 9 bolts, the sample standard deviation is .3 inches. How many bolts should be sampled in order to make us 95% confident that the sample mean bolt length is within .02 inches of the true mean bolt length? (1.96(0.3)/0.02)2 = 865 80 1470 3989 1197 27. The changing ecology of the swamps in Louisiana has been the subject of much environmental research. One water-quality parameter of concern is the total phosphorous level. Suppose that the EPA makes 15 measurements in one area of the swamp, yielding a mean level of total phosphorus of 12.3 parts per billion (ppb) and a standard deviation of 5.4 ppb. The EPA wants to test whether the data support the conclusion that the mean level is less than 15 ppb. Calculate the appropriate test statistic to test the hypotheses. Test Statistic = [ 12.3 - 15 ] / [ 5.4/sqrt(15) ] 7.50 1.94 3.88 -1.94 -7.50 28. If the sampled population has a mean 48 and standard deviation 16, then the mean and the standard deviation for the sampling distribution of X-bar (sample mean) for n=64 4 and 4 12 and 4 48 and 2 48 and 1/4 48 and 16 29. When we carry out a chi-square test of independence, as the difference between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable Decreases Increases May increase or decrease depending on the number of rows and columns Will be unaffected 30. The mean life of pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months? 1,000,000P(Life < 36) = 1,000,000P(Z < (36-40)/8) 500,000 808,500 191,500 308,500 31. A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 8. Only 5% of the students taking the test scored higher than what grade? (Show moderate work) P(Score > x) = 0.05 = P(Z > (x-69)/8) x = 69+1.64485(8) = 82.2 32. Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Deviation Constant 41.225 6.380 X1 1.081 1.353 X2 -18.404 4.547 Analysis of Variance Source DF SS Regression 2 2270.11 Error 26 3585.75 What is the number of Observations in the sample? 29 Write the least squares regression (prediction) equation. Y = 41.225 + 1.081X1 - 18.404X2 Test the usefulness of variable x2 in the model at alpha =.05. Calculate the t statistic and state your conclusions. Test statistic = -18.404/4.547 = -4.05 t(0.025,26) = -2.056 Conclude X2 is useful at alpha = 0.05. 33. A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66 at 5% and 10% significance levels. Indicate which test you are performing; One-proportion z-test show the hypotheses, H0: p ≤ 0.66 Ha: p > 0.66 the test statistic Test Statistic = ( 0.680 - 0.66 ) / sqrt( 0.66 ( 0.34 )/1500 ) = 1.635 and the critical values 5% critical value = z(0.95) = 1.645 10% critical value = z(0.9) = 1.282 and mention whether one-tailed or two-tailed. One-tailed Conclude: Not significantly greater than 0.66 at 5%. Significantly greater than 0.66 at 10%. 34. (I tried to put all the signs in here… they may not come in properly.. I can maybe send them to you another way?) Test H0: pi1 – pi2 <=.01, HA : pi1 – pi2 > .01 at alpha =.05 where p1 =.08, p2 =.035, n1 = 200, n2 = 400. Indicate which test you are performing; 2-proportion z-test show the test statistic Standard error of p difference = sqrt[ 0.08(0.92)/200+0.035(0.965)/400 ] = 0.0213 Test Statistic = ( 0.080 - 0.035 - 0.01) / 0.0213 = 1.643 and the critical values Critical value = z(0.95) = 1.6449 and mention whether one-tailed or two-tailed. One-tailed Conclusion: Do not reject H0. 35. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is known to be normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. Between what two values (in ounces) symmetrically distributed around the population mean will 80% of the apples fall? xL = 2.25 - 1.282(0.15) = 2.06 xU = 2.25 + 1.282(0.15) = 2.44 Between 2.06 ounces and 2.44 ounces. 36. The weight of a product is normally distributed with a standard deviation of .5 ounces. What should the average weight be if the production manager wants no more than 10% of the products to weigh more than 4.8 ounces? P(X > 4.8) ≤ 0.10 =P(Z > (4.8-average)/0.5) ≤ 0.10 Average ≤ 4.8-1.282(0.5) = 4.16 ounces 37. An insurance company estimates 35 percent of its claims have errors. The insurance company wants to estimate with 90 percent confidence the proportion of claims with errors. What sample size is needed if they wish to be within 5 percentage points of the actual? 0.35(0.65)(1.6449/0.05)2 = 247 38. A human resource manager is interested in whether absences occur during the week with equal frequency. The manager took a random sample of 100 absences and created the following table: Monday 28 Tuesday 20 Wednesday 12 Thursday 18 Friday 22 At a significance level of alpha = .05 test the Null that the probabilities of absences are the same for all five days. 2 2 2 2 2 [(28-20) +(20-20) +(12-20) +(18-20) +(22-20) ]/20 = 6.8 2 χ (0.05,4) = 9.488 Conclude the probabilities of absences are equal for all 5 days. 39. At a recent meeting of educational researchers comparison were made between the type of college freshmen attend and the numbers who drop out. A random sample of freshmen show the following results: (keep two decimals in calculating expected frequencies) 4Yr public 4Yr private 2Yr public 2Yr private drop out 10 9 15 9 don't drop 26 28 18 27 Use a significance level of .05 and determine if the type of school and the drop out rate are independent. 40. A small town has a population of 15,000 people. Among these 1,500 regularly visit a popular local bar. A sample of 225 people from those who regularly visit the bar is surveyed for their annual expenditures in the bar. It is found that on average each person who regularly visits the bar spends about $2000 per year in the bar with a standard deviation of $196. Construct a 99 percent confidence interval around the mean annual expenditure in the bar.