e270 homework 8 final
COMPREHENSIVE HOMEWORK PROBLEMS ? In occupied with doing statistical evaluation, the pattern imply must be interpreted as: a a fixed worth that is the same as the inhabitants imply.  When achieved, save as, utilizing your final identify and first identify, b a fixed worth that's roughly equal to the inhabitants imply. e270Lastname Firstname HW FINAL c a random variable that's roughly equal to the inhabitants imply when sampling is achieved with out substitute and e-mail it to stowfig@iupui.edu d a random variable that's roughly equal to the inhabitants imply if n > 30 and when sampling is completed with out substitute.  e a random variable that when averaged throughout many samples is roughly equal to the inhabitants imply. 2 Which of the next are random?  a x? after a pattern is taken b x? earlier than a pattern is taken c µ after a pattern is taken  d µ earlier than a pattern is taken  e Greater than one reply is appropriate.  three The month-to-month earnings of academics is generally distributed with a imply of $three,000 and the usual deviation of $250. We choose a pattern of 87 academics. The sampling distribution of the pattern imply has an anticipated worth and commonplace deviation of: a three,000 and 26.eight  b three,000 and 1.69  c three,000 and 250  d three,000 and 2.87  e three,000 and 321.6  four The following information was collected by taking a easy random pattern of a inhabitants  13 15 14 16 12  From this we all know that, a The inhabitants imply is 14.  b The purpose estimate of the inhabitants imply is 14.  c The inhabitants imply have to be 14 because the pattern imply is 14.  d Each a. and b. are appropriate.  e Each a., b., and c. are appropriate.  5 A direct mail firm needs to estimate the proportion of individuals on a big mailing listing that can buy a product. Suppose the true proportion is Zero.07. If 486 are sampled, what's the likelihood that the pattern proportion will differ from the inhabitants proportion inside ±Zero.03?  a Zero.024 b Zero.1428  c Zero.4952  d Zero.9994  e None of the above solutions is appropriate.  6 A high quality management knowledgeable needs to check automotive engines. The manufacturing supervisor claims they've a median lifetime of 92 months with a typical deviation of eight. If the declare is true, what's the likelihood that the imply engine life can be better than 90.eight months in a pattern of 93 engines? a Zero.0596  b Zero.0735  c Zero.4265  d Zero.5596  e Zero.9265  7 Growing the scale of a pattern from 100 to 200 will a scale back the usual error of the imply to one-half its unique worth. b haven't any impact on the usual error of the imply. c scale back the usual error of the imply to roughly 70% of its present worth. d double the usual error of the imply. e None of the above solutions is appropriate. NEXT TWO ARE RELATED QUESTIONS ABOUT SAMPLING DISTRIBUTIONS. 100 samples of dimension 85 every are drawn from an unknown inhabitants distribution of x and a pattern imply is calculated for every pattern. eight If the variety of samples stays at 100, however the dimension of every pattern is elevated from 85 to 125, then one would count on the variation in pattern means noticed throughout samples to: a enhance. b lower. c stay roughly the identical. d change a lot, however not essential enhance or lower. e be just like the variation of x values within the inhabitants. 9 If the variety of samples stays at 100, however the dimension of every pattern is elevated from 85 to 125, then one would count on the distribution of pattern means noticed throughout samples to: a stay unknown. b to rely upon the inhabitants distribution of x. c approximate the conventional distribution, however no more intently than when 100 samples have been drawn. d much less intently approximate the conventional distribution. e extra intently approximate the conventional distribution. 10 Annual part-time earnings within the U.S. common $15,000 and have a typical deviation $three,000. A pattern of 62 part-time earners is chosen. The usual error of the pattern imply is: a $5 b $7 c $48 d $242 e $381 11 A speedboat engine firm makes engines with the next specs: the engine delivers a median energy of 220 horsepower with a typical deviation of 16. Assuming that horsepower is generally distributed, if a randomly chosen single engine is examined, what's the likelihood that the horsepower will exceed 224? a Zero.4013 b Zero.3783 c Zero.3520 d Zero.3300 e Zero.2643 12 Within the earlier query, if a pattern of 80 engines are examined. What's likelihood that the pattern imply will exceed 222 horsepower. a Zero.4483 b Zero.3446 c Zero.2148 d Zero.1314 e Zero.1056 13 Take into account the horsepower common and commonplace deviation in query 2: µ = 220 and ? = 16. If the pattern dimension is n = 100, within the sampling distribution of x? what interval of x? values would include 95% of all pattern means? a 205.98 to 234.02 b 210.08 to 229.92 c 212.99 to 227.01 d 215.57 to 224.43 e 216.86 to 223.14 14 In accordance to the central restrict theorem, because the pattern dimension will increase, a the anticipated worth of x? approaches Zero. b the anticipated worth of ordinary error of x? approaches 1. c the commonplace error of x? approaches the inhabitants commonplace deviation. d the distribution of x? approaches the conventional. e the distribution of s, the pattern commonplace deviation, approaches Zero. 15 The precise proportion of faulty denims in a big warehouse is Zero.20. What's the likelihood that in a random pattern of 500 denims the pattern proportion p? might be inside a margin of ±Zero.04 of the inhabitants proportion of faulty denims? a Zero.8198 b Zero.8415 c Zero.8859 d Zero.9164 e Zero.9749 16 Within the earlier query, what interval of p? values comprises 90% of all p?’s? a Zero.171 to Zero.229 b Zero.165 to Zero.235 c Zero.154 to Zero.246 d Zero.145 to Zero.255 e Zero.122 to Zero.278 17 A pattern of 64 sufferers in a walk-in clinic confirmed that they needed to wait a median of 48 minutes earlier than they may see a health care provider. The pattern commonplace deviation was 20 minutes. What's the 95% confidence Interval for the inhabitants common ready time? a 45.2 50.eight b 44.6 51.four c 43.1 52.9 d 42.2 53.eight e 41.eight 54.2 18 What's the minimal pattern dimension to estimate the 95% confidence interval within the earlier query to inside plus or minus three minutes. Use a planning worth of 20 minutes for the usual deviation. a 131 b 141 c 151 d 161 e 171 19 Here's a downside just like the earlier query, however now the pattern of sufferers is solely 9. On this pattern the sufferers needed to wait a median of 45 minutes and the pattern commonplace deviation was 12 minutes. What's the margin of error for a 95% confidence Interval for the inhabitants common ready time? (Assume that the inhabitants of the ready instances in regular). a 7.eight b 9.2 c 10.6 d 12.Zero e 13.four 20 Think about 526 statisticians every took a special random pattern of the inhabitants of sufferers visiting the walk-in clinic in Query 17 (every took a pattern dimension of 64). About what number of would produce confidence intervals that contained the inhabitants imply? a 100 b 500 c Virtually all of them d All of them. e Can't inform primarily based on the data supplied. 21 To construct a confidence interval for the common age of the civilian labor pressure, a pattern of 100 individuals was chosen. The pattern imply was 38.5 years and the usual deviation was 13.2 years. The decrease and higher boundaries of a 95% confidence interval are: a 37.eight to 39.2 b 37.four to 39.6 c 36.three to 40.7 d 35.9 to 41.1 e 34.four to 42.6 22 We are able to make a confidence interval extra exact (narrower) by, a rising the pattern dimension. b lowering the boldness degree (or confidence coefficient). c rising the boldness degree d Each (a) and (b) are appropriate. e Each (a) and (c) are appropriate. 23 To estimate the inhabitants common age of the civilian labor pressure to inside a margin of error of Zero.5 years at 95% degree of confidence, what's the minimal pattern dimension? Assume the inhabitants commonplace deviation is understood to be 12.1 years. a 2,250 b 2,145 c 1,972 d 1,576 e 1,255 24 Utilizing the commonplace deviation 2.61 as a planning worth, what pattern dimension must be utilized in order to acquire a 95% confidence interval with a margin of error of ±Zero.5? a 105 b 94 c 85 d 64 e 56 25 To construct an interval estimate of commuting time from Fishers to downtown Indianapolis in a midweek rush hour interval 5 trial runs have been made, acquiring the next outcomes (in minutes). 55 45 43 34 38 Assuming the inhabitants commuting time is generally distributed, construct a 95% confidence interval for the inhabitants imply commuting time. The interval is: a 28.6 to 57.four b 29.9 to 56.1 c 31.2 to 54.eight d 33.1 to 52.9 e 36.Zero to 50.Zero 26 For one other interval estimate of the commuting time a pattern of 100 trial runs have been made. The decrease and higher bounds of the interval have been: L = 43.67 and U = 48.33 minutes. The pattern commonplace deviation was s = 10 minutes. What's the confidence degree for this interval estimate? a 98 %. b 96 %. c 94 %. d 92 %. e 90 %. 27 A survey of 200 people who accomplished 4 years of school confirmed that 36 smoked frequently. Utilizing this survey outcome what is the 95% confidence interval for the proportion of all people with 4 years of school training who smoke? a Zero.Zero97 to Zero.263 b Zero.107 to Zero.253 c Zero.127 to Zero.233 d Zero.137 to Zero.223 e Zero.147 to Zero.213 28 Within the earlier query, what's the minimal pattern dimension to estimate the inhabitants proportion of all people with 4 years of school training who smoke to inside a margin of error of ±Zero.03. We count on 19 out of each 20 such interval estimates to include the inhabitants proportion. Use the pattern proportion in the earlier query because the planning worth. a 227 b 355 c 631 d 993 e 1418 29 The director of admission at a big state college advises dad and mom of incoming college students about the price of textbooks throughout a typical semester. A pattern of 100 college students enrolled within the college signifies a pattern imply value of $315.40 with a pattern commonplace deviation of $69. The pattern is used to check the speculation that the inhabitants imply is at most $300. Which of the next is the proper assertion of the null and different hypotheses? a H0 : µ ? 300 H1 : µ < 300 b H0 : µ > 300 H1 : µ ? 300 c H0 : µ ? 300 H1 : µ > 300 d H0 : µ < 300 H1 : µ ? 300 e H0 : µ = 300 H1 : µ ? 300 30 Regardless how you answered the previous question, which of the following statements is correct? a If the mean cost of text books is in fact greater than $300 and the hypothesis test leads you to conclude that it is at most $300, the you have committed a Type II error. b If the mean cost of text books is in fact greater than $300 and the hypothesis test leads you to conclude that it is at most $300, the you have committed a Type I error. c If the mean cost of text books is at most $300 and the hypothesis test leads you to conclude that it is greater than $300, the you have committed a Type II error. d If the mean cost of text books is in less than $300 and the hypothesis test leads you to conclude that it is greater than $300, the you have committed a Type II error. e If the mean cost of text books is in less than $300 and the hypothesis test leads you to conclude that it is at least $300, the you have committed a Type II error. 31 Test H0 : µ ? 5,000 versus H1 : µ > 5,000 when a pattern of dimension 100 yields a imply of 5,315.four and a typical deviation of 1400. Conduct the take a look at with a likelihood of kind I error = Zero.10. Additionally compute the likelihood worth. Which of the next is the proper resolution: a The likelihood worth is Zero.02. Don't reject the null speculation that the imply is lower than or equal to 5000. b The likelihood worth is Zero.10. Don't reject the null speculation that the imply is lower than or equal to 5000. c The likelihood worth is Zero.02. Reject the null speculation that the imply is much less than or equal to 5000. d The likelihood worth is Zero.01. Conclude that the imply is lower than 5000. e The likelihood worth is Zero.01. Conclude that the imply is larger than 5000. 32 The vehicle producer Toyonda substitutes a special engine in vehicles of a mannequin that have been identified to have a median miles per gallon (mpg) ranking of 30 on the freeway. To check whether or not the brand new engine modifications the common mpg, a random pattern of 100 trial runs offers x? = 28.three mpg and s = 6.6 mpg. At ? = Zero.05 degree of significance, is the common freeway mpg ranking for brand new engines completely different from the ranking for the outdated engines? a The standardized take a look at statistic exceeds the essential worth. The typical freeway mpg ranking for brand new engines is completely different from that of the outdated engines. b The likelihood worth is lower than the extent of significance. The typical freeway mpg ranking for brand new engines is completely different from that of the outdated engines. c The standardized take a look at statistic exceeds the essential worth. The typical freeway mpg ranking for brand new engines is NOT completely different from that of the outdated engines. d The likelihood worth is larger than the extent of significance. The typical freeway mpg ranking for brand new engines is NOT completely different from that of the outdated engines. e Each (a) and (b) are appropriate. 33 The engineering group of Honota Motors has designed a brand new engine for vehicles of Mannequin X240 which it claims will enhance (enhance) the gasoline mileage whereas sustaining the identical horsepower. The present common freeway mileage is 25 mpg. A pattern of 40 trial runs offers x? = 26.four mpg. Primarily based on the common trial-run mpg the administration rejects the engineering team’s declare and doesn't undertake the brand new design. Suppose the brand new design does in truth enhance the gasoline mileage. Which of the next appropriately describes the management’s resolution: a The administration has rejected a real null speculation. Due to this fact, it has dedicated a Sort I Error. b The administration has rejected a real null speculation. Due to this fact, it has dedicated a Sort II Error. c The administration has not rejected a false different speculation. Due to this fact, it has dedicated a Sort I Error. d The administration has not rejected a false null speculation. Due to this fact, it has dedicated a Sort II Error. e Each (a) and (c) are appropriate. 34 Use the pattern of commuting instances from Fishers to downtown Indianapolis in a midweek rush hour interval: 55 45 43 34 38 Carry out a take a look at of speculation that the common time exceeds 36 minutes, utilizing ? = Zero.05. Primarily based on the pattern information, a The take a look at statistic is 1.964 and the essential worth is 1.64. The pattern imply is considerably better than 36. Reject the null speculation. b The take a look at statistic is 1.64 and the essential worth is 1.964. The pattern imply isn't considerably better than 36. Don't reject the null speculation. c The take a look at statistic is 1.Zero74 and the essential worth is 1.64. The pattern imply isn't considerably much less than 50. Don't reject the null speculation. d The take a look at statistic is 1.Zero74 and the essential worth is 2.132. The pattern imply isn't considerably above 35. Don't reject the null speculation. e The take a look at statistic is 1.964 and the essential worth is 2.132. The pattern imply isn't considerably above 36. Don't reject the null speculation. 35 To check the speculation that the proportion of people with 4 years of school training who smoke has decreased from 21% a decade in the past, a random pattern of 1200 such people revealed that 222 smoked. Use ? = Zero.05. Primarily based on the pattern outcome, a The pattern proportion isn't considerably lower than 21%. Don't reject the null speculation. Conclude that the proportion of school educated people who smoke has not decreased in comparison with a decade in the past. b The pattern proportion is considerably lower than 21%. Reject the null speculation. Conclude that the proportion of school educated people who smoke has decreased in comparison with a decade in the past. c The pattern proportion is considerably lower than 21%. Don't reject the null speculation. Conclude that the proportion of school educated people who smoke has decreased in comparison with a decade in the past. d The pattern proportion isn't considerably lower than 21%. Reject the null speculation. Conclude that the proportion of school educated people who smoke has not decreased in comparison with a decade in the past. e The take a look at statistic is lower than the essential worth. Don't reject the null speculation. Conclude that the proportion of school educated people who smoke has not decreased in comparison with a decade in the past. 36 Within the earlier query, the likelihood worth is: a Zero.Zero95 b Zero.032 c Zero.017 d Zero.Zero10 e Zero.004 NEXT THREE QUESTIONS ARE BASED ON THE FOLLOWING SCENARIO: The professors at Funds College make $75,000 on common. The professors need to persuade the Funds directors that professors from comparable universities make greater salaries. The Funds professors acquire pattern information on salaries from comparable universities to offer a take a look at of their speculation. 37 The normal type of the take a look at must be a H0: ? = $75,000 H1: ?.? $75,000 b H0: ? ? $75,000 H1: ? = $75,000 c H0: ? ? $75,000 H1: ? ? $75,000 d H0: ? ? $75,000 H1: ? > $75,000 e H0: ? ? $75,000 H1: ?< $75,000 38 If the Funds professors economists to make use of a 1 % significance degree as a substitute of a 5 % significance degree, the essential worth (s) might be _______ in absolute worth and it's _______ probably that the null speculation might be rejected. a bigger, extra b bigger, much less c smaller, extra d smaller, much less e unaffected, equally 39 The economists resolve to make use of a 1 % significance degree. They acquire pattern information on salaries from 20 comparable universities. The pattern imply is $81,000 and the pattern commonplace deviation is $10,000. The take a look at statistic is ________, which causes them to ________ the null speculation. a z = 2.68, reject b t = 2.68, fail to reject c z = Zero.81, reject d t = Zero.81, fail to reject e t = 2.68, reject NEXT FIVE QUESTIONS ARE BASED ON THE FOLLOWING REGRESSION OUTPUT: The next information for a pattern of 10 people exhibits the hourly earnings and years of education. Hourly EarningsYears of Education 17.24 15 15.00 16 14.91 eight four.50 6 18.00 15 6.29 12 19.23 12 18.69 18 7.21 12 42.06 20 The next regression Abstract Output is used to check the relationship between hourly earnings and years of education: SUMMARY OUTPUT Regression Statistics A number of R Zero.7311 R Sq. Adjusted R Sq. Zero.4763 Commonplace Error Observations 10 ANOVA df SS MS F Significance F Regression 1 538.40905 9.1853643 Zero.0162912 Residual eight 468.93 Complete 9 1007.34 Coefficients Std Error t Stat P-valueLower 95% Higher 95% Intercept -7.791 eight.3134 -Zero.93710.3761 -26.96211.38 X Variable 1 1.799 Zero.5935 Zero.0163 Reply the subsequent FIVE questions utilizing the data within the Abstract Output. 40 What's the expected hourly earnings for 12 years of education? a three b 6.6 c 13.eight d 19.19 e 24.59 41 What proportion of hourly earnings is defined by years of education? a 74.60% b 73.10% c 69.30% d 53.40% e 47.60% 42 What's the 95% confidence interval for the inhabitants slope parameter ?1? a Zero.eight 2.eight b Zero.43 three.17 c Zero.23 three.37 d Zero.13 three.47 e Zero.03 three.57 43 To carry out a take a look at of speculation that the inhabitants slope parameter ?1 is zero, the take a look at statistic is: a three.Zero31 b 2.306 c 2.262 d 2.228 e Zero.33 44 Given the P-value of Zero.0163, we will conclude, at 5% degree of significance, that: a The inhabitants slope parameter is zero. There's NO relationship between hourly earnings and years of education. b The inhabitants slope parameter is completely different than zero. There's NO relationship between hourly earnings and years of education. c The inhabitants slope parameter is completely different than zero. There's a relationship between hourly earnings and years of education. d The inhabitants slope parameter is zero. There's a relationship between hourly earnings and years of education. e There's a small likelihood of a Sort II error, accepting the speculation that the slope parameter isn't equal to zero, when in truth it's. To check the connection between manufacturers’ market share and the standard of product. The following information on market share (in proportion) and product high quality (scores on the size of Zero to 100) can be found. The query is, are the variations in market share defined by the high quality of the product? Market share Product High quality (%) (Scale: Zero to 100) 2 27 three 39 10 73 9 66 four 33 6 43 5 47 eight 55 7 60 9 68 Utilizing the next calculations full the related elements (the shaded cells) of the Excel regression output beneath and reply FOUR questions. y? = 6.three x? = 51.1 ?xy = three,592 ?x² = 28,331 ?(x ? x?)(y ? y?) = 372.7 ?(x ? x?)² = 2218.9 SUMMARY OUTPUT Regression Statistics A number of R R Sq. Adjusted R Sq. Commonplace Error Observations ANOVA df SS MS F Significance F Regression Residual 5.499 Complete 68.10 Coefficients Std Error t Stat P-valueLower 95% Higher 95% Intercept X Variable 1 45 The predicted market share for a product high quality ranking of 90 is: a 11.2 b 12.eight c 13.four d 13.9 e 14.four 46 The proportion of the variations in market share defined by product high quality ranking is: a Zero.96 b Zero.92 c Zero.86 d Zero.82 e Zero.78 47 The higher boundary of the 95% confidence interval for the inhabitants slope parameter is: a Zero.241 b Zero.235 c Zero.228 d Zero.209 e Zero.117 48 The t Stat for the take a look at of speculation that the inhabitants slope parameter is zero is: a 2.95 b 7.65 c 9.54 d 10.11 e 10.98 Subsequent THREE questions use the next information describing the median annual household earnings (in $1000s) and the median sale value of a home (in $1000s) for a pattern of 12 housing markets. The information are used to regress the median value in a housing market on the median earnings in that market. The regression output follows the info. IncomePrice Market ($1000s) ($1000s) Syracuse, NY 41.eight 76 Springfield, IL 47.7 91 Lima, OH 40.Zero 65 Dayton, OH 44.three 88 Beaumont, TX 37.three 70 Lakeland, FL 35.9 73 Baton Rouge, LA 39.three 85 Nashua, NH 56.9 118 Racine, WI 46.7 81 Des Moines, IA48.three 89 Minneapolis 54.6 110 Wilmington, DE-MD 55.5 110 Common 45.692 SUMMARY OUTPUT Regression Statistics A number of R R Sq. Adjusted R Sq. Commonplace Error Observations ANOVA df SS MS F Significance F Regression 2717.86 Residual Complete 3158 Coefficients Std Error t Stat P-value Intercept -11.802 X Variable 1 2.1843 49 The purpose estimate of the median value in a housing market with a median household earnings of $50,270 every year is: a $97,000 b $98,000 c $97,270 d $98,990 e $99,000 50 What % of the full variation within the median sale value of homes is defined by the estimated regression line? a 93 b 84 c 63 d 86 e 80 51 The sum of squared deviations x’s is: ?(x ? x?)² = 569.669. Calculate the t statistic for testing the null speculation of no linear relation (i.e. the slope parameter is zero) at a 10% degree of significance (assume that the errors are regular, so there isn't a downside utilizing the t distribution). The conclusion can be: a reject the null speculation; there's a vital linear relationship. b don't reject the null speculation; there isn't a vital linear relationship. c reject the null speculation; there isn't a vital linear relationship. d don't reject the null speculation; there's a vital linear relationship. e reject the null speculation at 10%; however you wouldn't reject at 1%.