6 week 7 homework Question 1 with table Question 2 with Question 3 with with data set Question 3 with with data set Question 4 with with table Data Sets Table question 1 None for question 2 Question 4 table Boiler Design Boiler Drum capacity, pressure, type, x3 type, x4 x1 x2 3,137 120,000 375 1 1 3,590 65,000 750 1 1 4,526 150,000 500 1 1 Hours, y 10,825 1,073,877 4,023 4,206 4,006 3,728 3,211 1,200 3,317 3,700 4,504 3,900 3,105 150,000 441,000 441,000 627,000 610,000 30,000 120,000 69,000 150,000 400,000 600,000 2,170 0 1 325 410 410 1,525 1,500 325 390 800 500 390 1,400 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1) . a) Option A; b) Option A; 2nd Option c) (1459.9, 2525.8); Option B d) Option D 2) . a) . 3) . a) Y = -77.527+ 0.004*X1+2.573*X2-0.042*X3 b) Yes; Less than c) (29.80, 59.82) 4) . a) Y = 1.86808+0.10195*X1+0.00011*X2 b) Option A; Options are cropped out so send them again; Option A c) (0.05366, 0.15024) d) y x1 1871 3223 2868 1558 1665 3968 2163 3006 1944 2881 x2 22 53 41 22 64 41 52 35 21 38 5 8 7 4 5 12 9 11 8 10 Final Exam - Final Exam Time Remaining: 02:18:02 Page: 1 2 3 Page 1 Question 1. 1. (TCO A) An assembly line worker samples 20 items off the line every hour and measures the width of each item (in units of inches). The results for one such hour are given here. 13.8 15.1 14.8 14.9 15.8 14.5 14.8 14.7 14.2 15.1 15.3 15.6 14.8 15.5 15.2 15.1 15.2 14.6 14.9 14.7 a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on width of items. b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33) Variable N N* Mean SE Mean StDev Variance Squares Minimum C1 20 0 14.930 0.105 0.468 0.219 4462.260 13.800 14.700 Variable Median Q3 Maximum Range Skewness C1 14.900 15.200 15.800 2.000 -0.42 mean = 14.930 median = 14.900 mode = 15.1 standard deviation = 0.468 Q1 =14.700 Q3 = 15.200 Q1 Min = 13.800 Max .= 15.800 b. In the context of this situation, interpret the Median, Q1, and Q3. The Lower quartile, Q1 is the 25th percentile : Q1 : 14.700 distance 1: Median - Q3 = 14.900 - 15.2 = 0.3 distance 2: Median - Q1 = 14.900 - 14.7= 0.2 The upper quartile, is the 75th percentile: Q3 : 15.200 Q3-Q1 is the interquantile range. the distance D1 between and median and Q3 is greater than that between the median and Q1, then we say distribution is be skewed to the right. D1 < D2 then we say The lower quartile, Q1= 14.7 is the 25th percentile. The upper quartile, Q3=15.2 is the 75th percentile. Q3-Q1 is the interquantile range. If the distance between and median and Q3 is greater than that between the median and Q1, the distribution may be skewed to the right. 25% of the values are less than or equal to Q1 : 14.7 50% of the values are less than or equal to Q2: 14.900 75% of the values are less than or equal to Q3: 15.2 Variable N N* Mean SE Mean StDev Variance Squares Minimum Q1 C1 20 0 14.930 0.105 0.468 0.219 4462.260 13.800 14.700 Variable Median Q3 Maximum Range Skew ness C1 14.900 15.200 15.800 2.000 -0.42 mean = 14.930 median = 14.900 mode = 15.1 standard deviation = 0.468 Q1 =14.700 Q3 = 15.200 Min = 13.800 Max .= 15.800 Question 2. 2. (TCO B) JR Trucking buys tires from three suppliers: Goodyear, Michelin, and Bridgestone. Data on the last 1,000 tires that were purchased are described in the table below. Defective Not Defective Total Goodyear 5 495 500 Michelin 6 294 300 Bridgestone 10 190 200 21 979 1000 Total If you choose a tire at random, then find the probability that the tire a. was made by Michelin. b. was made by Goodyear and was defective. c. was not defective, given that the tire was made by Bridgestone. (Points : 18) a-P(A) = 300/1000=.3 b-P (a)= 500/1000= .005 c-P(A)= 190/979= .194 Question 3. 3. (TCO B) Historically, 70% of your customers at Rodale Emporium pay for their purchases using credit cards. In a sample of 20 customers, find the probability that a. exactly 14 customers will pay for their purchases using credit cards. b. at least 10 customers will pay for their purchases using credit cards. c. at most 12 customers will pay for their purchases using credit cards. (Points : 18) a- P(x=14) n= 20 p =0.7 : = 0.191639 B- P(X>=10) = 1- P(9) = 1- .0171448 = 0.9828552 c- P(X<=12) = 0.227728 Question 4. 4. (TCO B) Fuel efficiency for cars made in the United States is normally distributed with a mean of 28.8 mpg and a standard deviation of 8.2 mpg. a. What percentage of cars made in the United States have fuel efficiency above 40 mpg? b. What percentage of cars made in the United States have fuel efficiency between 25 and 35 mpg? c. A special tax credit is planned for the best (highest) 8% of cars made in the United States in terms of fuel efficiency. How high must the fuel efficiency be in order to qualify for this special tax credit? (Points : 18) Question 5. 5. (TCO C) A large-sized bag of Neato Chips should contain 16 oz of potato chips. A sample of 50 large-sized bags is selected with the following results. Sample Size = 50 Sample Mean = 15.85 oz Sample Standard Deviation = 1.53 oz a. Construct a 95% confidence interval for the mean amount of contents per bag. . b. Interpret this interval. c. How large a sample size will need to be selected if we wish to have a 99% confidence interval with a margin for error of .10 oz? (Points : 18) Question 6. 6. (TCO C) A marketing research firm wishes to estimate the proportion of adults who are planning to buy a new car in the next 6 months. A simple random sample of 100 adults led to 22 who were planning to buy a new car in the next 6 months. a. Compute the 95% confidence interval for the proportion of adults who are planning to buy a new car in the next 6 months. b. Interpret this confidence interval. c. How large a sample size will need to be selected if we wish to have a 95% confidence interval that is accurate to within 1%. (Points : 18) Question 7. 7. (TCO D) Persons living near a smelting plant have complained that the plant violates the city's noise pollution code. The code states that to be in compliance, noise levels are only allowed to exceed 120 decibels less than 10% of the time. You monitor the noise levels at 150 randomly selected times and found that 11 were above 120 decibels. Does the sample data provide evidence to conclude that the plant is in compliance with the noise pollution code (with = .05)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the plant is in compliance with the noise pollution code (with = .05)? (Points : 24) Question 8. 8. (TCO D) A restaurant franchise company has a policy of opening new restaurants only in areas that have a mean household income in excess of $65,000. The company is currently considering an area to open a new restaurant. A random sample of 144 households from this area is selected yielding the following results. Sample Size = 144 Sample Mean = $66,124 Sample Standard Deviation = $7,400 Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (using = .05)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (using = .05)? (Points : 24) Page: 1 2 3 Time Remaining: 02:18:02 ahmad nijim Dec 16 (8 days ago) to Anubhav On Mon, Dec 16, 2013 at 7:19 PM, ahmad nijim wrote: Week 8 : Final Exam - Final Exam Time Remaining: 02:18:02 Page: 1 2 3 Page 1 Question 1. 1. (TCO A) An assembly line worker samples 20 items off the line every hour and measures the width of each item (in units of inches). The results for one such hour are given here. 13.8 15.1 14.8 14.9 15.8 14.5 14.8 14.7 14.2 15.1 15.3 15.6 14.8 15.5 15.2 15.1 15.2 14.6 14.9 14.7 a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on width of items. b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33) Variable N N* Mean SE Mean StDev Variance Squares Minimum Q1 C1 20 0 14.930 0.105 0.468 0.219 4462.260 13.800 14.700 Variable Median Q3 Maximum Range Skew ness C1 14.900 15.200 15.800 2.000 -0.42 mean = 14.930 median = 14.900 mode = 15.1 standard deviation = 0.468 Q1 =14.700 Q3 = 15.200 Min = 13.800 Max .= 15.800 Question 2. 2. (TCO B) JR Trucking buys tires from three suppliers: Goodyear, Michelin, and Bridgestone. Data on the last 1,000 tires that were purchased are described in the table below. Defective Goodyear Not Defective Total 5 495 500 Michelin 6 294 300 Bridgestone 10 190 200 21 979 1000 Total If you choose a tire at random, then find the probability that the tire a. was made by Michelin. b. was made by Goodyear and was defective. c. was not defective, given that the tire was made by Bridgestone. (Points : 18) a-P(A) = 300/1000=.3 b-P (a)= 500/1000= .005 c-P(A)= 190/979= .194 Question 3. 3. (TCO B) Historically, 70% of your customers at Rodale Emporium pay for their purchases using credit cards. In a sample of 20 customers, find the probability that a. exactly 14 customers will pay for their purchases using credit cards. b. at least 10 customers will pay for their purchases using credit cards. c. at most 12 customers will pay for their purchases using credit cards. (Points : 18) a- P(x=14) n= 20 p =0.7 : = 0.191639 B- P(X>=10) = 1- P(9) = 1- .0171448 = 0.9828552 c- P(X<=12) = 0.227728 Question 4. 4. (TCO B) Fuel efficiency for cars made in the United States is normally distributed with a mean of 28.8 mpg and a standard deviation of 8.2 mpg. a. What percentage of cars made in the United States have fuel efficiency above 40 mpg? b. What percentage of cars made in the United States have fuel efficiency between 25 and 35 mpg? c. A special tax credit is planned for the best (highest) 8% of cars made in the United States in terms of fuel efficiency. How high must the fuel efficiency be in order to qualify for this special tax credit? (Points : 18) Question 5. 5. (TCO C) A large-sized bag of Neato Chips should contain 16 oz of potato chips. A sample of 50 large-sized bags is selected with the following results. Sample Size = 50 Sample Mean = 15.85 oz Sample Standard Deviation = 1.53 oz a. Construct a 95% confidence interval for the mean amount of contents per bag. . b. Interpret this interval. c. How large a sample size will need to be selected if we wish to have a 99% confidence interval with a margin for error of .10 oz? (Points : 18) Question 6. 6. (TCO C) A marketing research firm wishes to estimate the proportion of adults who are planning to buy a new car in the next 6 months. A simple random sample of 100 adults led to 22 who were planning to buy a new car in the next 6 months. a. Compute the 95% confidence interval for the proportion of adults who are planning to buy a new car in the next 6 months. b. Interpret this confidence interval. c. How large a sample size will need to be selected if we wish to have a 95% confidence interval that is accurate to within 1%. (Points : 18) Question 7. 7. (TCO D) Persons living near a smelting plant have complained that the plant violates the city's noise pollution code. The code states that to be in compliance, noise levels are only allowed to exceed 120 decibels less than 10% of the time. You monitor the noise levels at 150 randomly selected times and found that 11 were above 120 decibels. Does the sample data provide evidence to conclude that the plant is in compliance with the noise pollution code (with = .05)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the plant is in compliance with the noise pollution code (with = .05)? (Points : 24) Question 8. 8. (TCO D) A restaurant franchise company has a policy of opening new restaurants only in areas that have a mean household income in excess of $65,000. The company is currently considering an area to open a new restaurant. A random sample of 144 households from this area is selected yielding the following results. Sample Size = 144 Sample Mean = $66,124 Sample Standard Deviation = $7,400 Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (using = .05)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (using = .05)? (Points : 24) Page: 1 2 3 Time Remaining: 02:18:02 Page 2 Question 1. 1. (TCO E) Ten Dodge Caravans were randomly selected from the classified ads. The following data gives the AGE (X, in years) and PRICE (Y, in $) for each of these 10 cars. AGE PRICE PREDICT 6 12500 4 6 11500 10 6 13000 2 26000 2 21900 5 15000 4 19000 5 16300 1 26000 4 16000 Correlations: AGE, PRICE Pearson correlation of AGE and PRICE = 0.968 PValue = 0.000 Regression Analysis: PRICE versus AGE The regression equation is PRICE = 29160 2790 AGE Predictor Coef SE Coef T P Constant 29160 1143 25.51 0.000 AGE 2790.3 256.3 10.89 0.000 S = 1424.65 RSq = 93.7% RSq(adj) = 92.9% Analysis of Variance Source DF SS MS F P Regression 1 240578913 240578913 118.53 0.000 Residual Error 8 16237087 2029636 Total 9 256816000 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 17999 451 (16958, 19040) (14553, 21445) 2 1257 1578 (2381, 4896) (3645, 6159)XX XX denotes a point that is an extreme outlier in the predictors. Values of Predictors for New Observations New Obs AGE 1 4.0 2 10.0 a. Analyze the above output to determine the regression equation. b. Find and interpret 1 in the context of this problem. c. Find and interpret the coefficient of determination (r-squared). d. Find and interpret coefficient of correlation. e. Does the data provide significant evidence (= .05) that age can be used to predict price? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret. f. Find the 95% confidence interval for mean price for all 4-year-old Caravans. Interpret this interval. g. Find the 95% prediction interval for the price of a 4-year-old Caravan. Interpret this interval. h. What can we say about the price of a 10-year-old Caravan? (Points : 48) a- The regression equation is PRICE = 29160 - 2790 AGE y = 29160 - 2790 X b-MS= 2029636 c- r-sq = 92.9 how much variation in the date that we are explaining r2 implies that only of the sample variation in number --- cases can be explained by using age in the straight-line model. Analysis of Variance d- 0.929 e- Since @ = .10 and P = 0.000 P<@ then we Reject H0 there is sufficient evidence, and we say that the slope is significant. f- 95% CI (16958, 19040) : we are 95% confident that the data mean for each unit change in the -X value is between the limits of the confidence level (16958, 19040) g. 95% PI (14553, 21445): is the prediction interval we say that we are 95% confident that for one more year there change is between the limits of the prediction interval h- we say that the slop s significant . -the slope of the line B1 for each unit increase in mean pore diameter , the mean is estimated to increase by B1(the change in number as we add age Question 8 : Time Remaining: 00:37:16 Page: 1 2 3 Page 2 Question 1. 1. (TCO E) Ten Dodge Caravans were randomly selected from the classified ads. The following data gives the AGE (X, in years) and PRICE (Y, in $) for each of these 10 cars. AGE PRICE PREDICT 6 12500 4 6 11500 10 6 13000 2 26000 2 21900 5 15000 4 19000 5 16300 1 26000 4 16000 Correlations: AGE, PRICE Pearson correlation of AGE and PRICE = 0.968 PValue = 0.000 Regression Analysis: PRICE versus AGE The regression equation is PRICE = 29160 2790 AGE Predictor Coef SE Coef T P Constant 29160 1143 25.51 0.000 AGE 2790.3 256.3 10.89 0.000 S = 1424.65 RSq = 93.7% RSq(adj) = 92.9% Analysis of Variance Source DF SS MS F P Regression 1 240578913 240578913 118.53 0.000 Residual Error 8 16237087 2029636 Total 9 256816000 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 17999 451 (16958, 19040) (14553, 21445) 2 1257 1578 (2381, 4896) (3645, 6159)XX XX denotes a point that is an extreme outlier in the predictors. Values of Predictors for New Observations New Obs AGE 1 4.0 2 10.0 a. Analyze the above output to determine the regression equation. b. Find and interpret 1 in the context of this problem. c. Find and interpret the coefficient of determination (r-squared). d. Find and interpret coefficient of correlation. e. Does the data provide significant evidence (= .05) that age can be used to predict price? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret. f. Find the 95% confidence interval for mean price for all 4-year-old Caravans. Interpret this interval. g. Find the 95% prediction interval for the price of a 4-year-old Caravan. Interpret this interval. h. What can we say about the price of a 10-year-old Caravan? (Points : 48) aThe regression equation is PRICE = 29160 - 2790 AGE y = 29160 - 2790 X b-MS= 2029636 c- r-sq = 92.9 how much variation in the date that w e are explaining r2 implies that only of the sample variation in number --- cases can be explained by using age in the straight-line model. Analysis of Variance d- 0.929 e- Since @ = .10 and P = 0.000 P<@ then w e Reject H0 there is The regression equation is Perceived_Recovery = 3.24 + 2.53 Blood_Lactate_Level ___ > y = 3.24 + 2.53 X 1-the slope of the line B1 for each unit increase in mean pore diameter , the mean is estimated to increase by B1(the change in number of --- as we add one factor ---X-- .) Predictor Coef SE Coef T P Constant 3.244 5.332 0.61 0.553 Blood_Lactate_Level 2.533 1.055 2.40 0.031 S = 4.53825 R-Sq = 29.2% R-Sq(adj) = 24.1% 2-R-Sq(adj) = 24.1% : how much variation in the date that we are explaining r2 implies that only 24.3% of the sample variation in number --- cases can be explained by using ----(x) in the straight-line model. Analysis of Variance Source DF SS MS F P 1 118.66 118.66 5.76 0.031 Residual Error 14 288.34 20.60 Total 15 407.00 Regression 3-confidenece level : New Obs Fit SE Fit 1 33553 5201 95% CI (21559, 45548) 95% PI (21227, 45880)XX a- 95% PI : is the prediction interval we say that we are 95% confident that the actual ---- accuracy ...... for each unit X change --- is between the limits of the prediction interval b- 95% CI : we are 95% confident that the mean of ...... for each unit change in the -X value -- is between the limits of the confidence level (22.22,33.3) . 4-Since @ = .10 and P = 0.031 P<@ then we Reject H0 there is sufficient evidence, and we say that the slope is significant. To find P-Value we go : Stat > Basic stat > correlation > choose display P-value Q8 : Y = -1339 + 86 numberID + 12.3 Age Find P > H0: b2 = 0 Ha: b2 0 Find T> H0: b1 =0 Ha: b1 0 R-Sq(adj)= 66% Means that the varation of price can be explained by the variation of the number of - and of --- PRICE = - 1339 + 12.7 AGE + 86.0 NUMBIDS For each one year increase of the --- age the price increases in average of 12.7 if we assumed that the number of piders is constant . 12.7 AGE : For each one increase of the --- piders numberthe price increases in average of 86 if we assumed that the number of Age is constant . 86.0 NUMBIDS: Q8: a. a. Ho: u = .500 Ha: p u <500 b. significance level is alpha .10 c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. z<-1.28 d. Z = -1.17 One-Sample Z Test of mu = 500 vs < 500 The assumed standard deviation = 84 90% Upper N Mean SE Mean Bound Z P 49 486.0 12.0 501.4 -1.17 0.122 e. Donot reject Ho f. This means that there's insufficent evidence to conclude the mean annual cdental expense. g. P value is 0.122 that means P>alpha we have .122> .10 that means don't reject Ho h. There 's insufficent evidence of sample data provide evidence (with a = 0.10), that the mean annual dental expense per employee is less than $500? \f\f\f\f\f\f\f\f\f Final Exam - Final Exam Time Remaining: 02:18:02 Page: 1 2 3 Page 1 Question 1. 1. (TCO A) An assembly line worker samples 20 items off the line every hour and measures the width of each item (in units of inches). The results for one such hour are given here. 13.8 15.1 14.8 14.9 15.8 14.5 14.8 14.7 14.2 15.1 15.3 15.6 14.8 15.5 15.2 15.1 15.2 14.6 14.9 14.7 a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on width of items. b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33) Variable N N* Mean SE Mean StDev Variance Squares Minimum C1 20 0 14.930 0.105 0.468 0.219 4462.260 13.800 14.700 Variable Median Q3 Maximum Range Skewness C1 14.900 15.200 15.800 2.000 -0.42 mean = 14.930 median = 14.900 mode = 15.1 standard deviation = 0.468 Q1 =14.700 Q3 = 15.200 Q1 Min = 13.800 Max .= 15.800 b. In the context of this situation, interpret the Median, Q1, and Q3. The Lower quartile, Q1 is the 25th percentile : Q1 : 14.700 distance 1: Median - Q3 = 14.900 - 15.2 = 0.3 distance 2: Median - Q1 = 14.900 - 14.7= 0.2 The upper quartile, is the 75th percentile: Q3 : 15.200 Q3-Q1 is the interquantile range. the distance D1 between and median and Q3 is greater than that between the median and Q1, then we say distribution is be skewed to the right. D1 < D2 then we say The lower quartile, Q1= 14.7 is the 25th percentile. The upper quartile, Q3=15.2 is the 75th percentile. Q3-Q1 is the interquantile range. If the distance between and median and Q3 is greater than that between the median and Q1, the distribution may be skewed to the right. 25% of the values are less than or equal to Q1 : 14.7 50% of the values are less than or equal to Q2: 14.900 75% of the values are less than or equal to Q3: 15.2 Variable N N* Mean SE Mean StDev Variance Squares Minimum Q1 C1 20 0 14.930 0.105 0.468 0.219 4462.260 13.800 14.700 Variable Median Q3 Maximum Range Skew ness C1 14.900 15.200 15.800 2.000 -0.42 mean = 14.930 median = 14.900 mode = 15.1 standard deviation = 0.468 Q1 =14.700 Q3 = 15.200 Min = 13.800 Max .= 15.800 Question 2. 2. (TCO B) JR Trucking buys tires from three suppliers: Goodyear, Michelin, and Bridgestone. Data on the last 1,000 tires that were purchased are described in the table below. Defective Not Defective Total Goodyear 5 495 500 Michelin 6 294 300 Bridgestone 10 190 200 21 979 1000 Total If you choose a tire at random, then find the probability that the tire a. was made by Michelin. b. was made by Goodyear and was defective. c. was not defective, given that the tire was made by Bridgestone. (Points : 18) a-P(A) = 300/1000=.3 b-P (a)= 500/1000= .005 c-P(A)= 190/979= .194 Question 3. 3. (TCO B) Historically, 70% of your customers at Rodale Emporium pay for their purchases using credit cards. In a sample of 20 customers, find the probability that a. exactly 14 customers will pay for their purchases using credit cards. b. at least 10 customers will pay for their purchases using credit cards. c. at most 12 customers will pay for their purchases using credit cards. (Points : 18) a- P(x=14) n= 20 p =0.7 : = 0.191639 B- P(X>=10) = 1- P(9) = 1- .0171448 = 0.9828552 c- P(X<=12) = 0.227728 Question 4. 4. (TCO B) Fuel efficiency for cars made in the United States is normally distributed with a mean of 28.8 mpg and a standard deviation of 8.2 mpg. a. What percentage of cars made in the United States have fuel efficiency above 40 mpg? b. What percentage of cars made in the United States have fuel efficiency between 25 and 35 mpg? c. A special tax credit is planned for the best (highest) 8% of cars made in the United States in terms of fuel efficiency. How high must the fuel efficiency be in order to qualify for this special tax credit? (Points : 18) Question 5. 5. (TCO C) A large-sized bag of Neato Chips should contain 16 oz of potato chips. A sample of 50 large-sized bags is selected with the following results. Sample Size = 50 Sample Mean = 15.85 oz Sample Standard Deviation = 1.53 oz a. Construct a 95% confidence interval for the mean amount of contents per bag. . b. Interpret this interval. c. How large a sample size will need to be selected if we wish to have a 99% confidence interval with a margin for error of .10 oz? (Points : 18) Question 6. 6. (TCO C) A marketing research firm wishes to estimate the proportion of adults who are planning to buy a new car in the next 6 months. A simple random sample of 100 adults led to 22 who were planning to buy a new car in the next 6 months. a. Compute the 95% confidence interval for the proportion of adults who are planning to buy a new car in the next 6 months. b. Interpret this confidence interval. c. How large a sample size will need to be selected if we wish to have a 95% confidence interval that is accurate to within 1%. (Points : 18) Question 7. 7. (TCO D) Persons living near a smelting plant have complained that the plant violates the city's noise pollution code. The code states that to be in compliance, noise levels are only allowed to exceed 120 decibels less than 10% of the time. You monitor the noise levels at 150 randomly selected times and found that 11 were above 120 decibels. Does the sample data provide evidence to conclude that the plant is in compliance with the noise pollution code (with = .05)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the plant is in compliance with the noise pollution code (with = .05)? (Points : 24) Question 8. 8. (TCO D) A restaurant franchise company has a policy of opening new restaurants only in areas that have a mean household income in excess of $65,000. The company is currently considering an area to open a new restaurant. A random sample of 144 households from this area is selected yielding the following results. Sample Size = 144 Sample Mean = $66,124 Sample Standard Deviation = $7,400 Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (using = .05)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (using = .05)? (Points : 24) Page: 1 2 3 Time Remaining: 02:18:02 ahmad nijim Dec 16 (8 days ago) to Anubhav On Mon, Dec 16, 2013 at 7:19 PM, ahmad nijim wrote: Week 8 : Final Exam - Final Exam Time Remaining: 02:18:02 Page: 1 2 3 Page 1 Question 1. 1. (TCO A) An assembly line worker samples 20 items off the line every hour and measures the width of each item (in units of inches). The results for one such hour are given here. 13.8 15.1 14.8 14.9 15.8 14.5 14.8 14.7 14.2 15.1 15.3 15.6 14.8 15.5 15.2 15.1 15.2 14.6 14.9 14.7 a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on width of items. b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33) Variable N N* Mean SE Mean StDev Variance Squares Minimum Q1 C1 20 0 14.930 0.105 0.468 0.219 4462.260 13.800 14.700 Variable Median Q3 Maximum Range Skew ness C1 14.900 15.200 15.800 2.000 -0.42 mean = 14.930 median = 14.900 mode = 15.1 standard deviation = 0.468 Q1 =14.700 Q3 = 15.200 Min = 13.800 Max .= 15.800 Question 2. 2. (TCO B) JR Trucking buys tires from three suppliers: Goodyear, Michelin, and Bridgestone. Data on the last 1,000 tires that were purchased are described in the table below. Defective Goodyear Not Defective Total 5 495 500 Michelin 6 294 300 Bridgestone 10 190 200 21 979 1000 Total If you choose a tire at random, then find the probability that the tire a. was made by Michelin. b. was made by Goodyear and was defective. c. was not defective, given that the tire was made by Bridgestone. (Points : 18) a-P(A) = 300/1000=.3 b-P (a)= 500/1000= .005 c-P(A)= 190/979= .194 Question 3. 3. (TCO B) Historically, 70% of your customers at Rodale Emporium pay for their purchases using credit cards. In a sample of 20 customers, find the probability that a. exactly 14 customers will pay for their purchases using credit cards. b. at least 10 customers will pay for their purchases using credit cards. c. at most 12 customers will pay for their purchases using credit cards. (Points : 18) a- P(x=14) n= 20 p =0.7 : = 0.191639 B- P(X>=10) = 1- P(9) = 1- .0171448 = 0.9828552 c- P(X<=12) = 0.227728 Question 4. 4. (TCO B) Fuel efficiency for cars made in the United States is normally distributed with a mean of 28.8 mpg and a standard deviation of 8.2 mpg. a. What percentage of cars made in the United States have fuel efficiency above 40 mpg? b. What percentage of cars made in the United States have fuel efficiency between 25 and 35 mpg? c. A special tax credit is planned for the best (highest) 8% of cars made in the United States in terms of fuel efficiency. How high must the fuel efficiency be in order to qualify for this special tax credit? (Points : 18) Question 5. 5. (TCO C) A large-sized bag of Neato Chips should contain 16 oz of potato chips. A sample of 50 large-sized bags is selected with the following results. Sample Size = 50 Sample Mean = 15.85 oz Sample Standard Deviation = 1.53 oz a. Construct a 95% confidence interval for the mean amount of contents per bag. . b. Interpret this interval. c. How large a sample size will need to be selected if we wish to have a 99% confidence interval with a margin for error of .10 oz? (Points : 18) Question 6. 6. (TCO C) A marketing research firm wishes to estimate the proportion of adults who are planning to buy a new car in the next 6 months. A simple random sample of 100 adults led to 22 who were planning to buy a new car in the next 6 months. a. Compute the 95% confidence interval for the proportion of adults who are planning to buy a new car in the next 6 months. b. Interpret this confidence interval. c. How large a sample size will need to be selected if we wish to have a 95% confidence interval that is accurate to within 1%. (Points : 18) Question 7. 7. (TCO D) Persons living near a smelting plant have complained that the plant violates the city's noise pollution code. The code states that to be in compliance, noise levels are only allowed to exceed 120 decibels less than 10% of the time. You monitor the noise levels at 150 randomly selected times and found that 11 were above 120 decibels. Does the sample data provide evidence to conclude that the plant is in compliance with the noise pollution code (with = .05)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the plant is in compliance with the noise pollution code (with = .05)? (Points : 24) Question 8. 8. (TCO D) A restaurant franchise company has a policy of opening new restaurants only in areas that have a mean household income in excess of $65,000. The company is currently considering an area to open a new restaurant. A random sample of 144 households from this area is selected yielding the following results. Sample Size = 144 Sample Mean = $66,124 Sample Standard Deviation = $7,400 Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (using = .05)? Use the hypothesis testing procedure outlined below. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the population mean annual household income is in excess of $65,000 (using = .05)? (Points : 24) Page: 1 2 3 Time Remaining: 02:18:02 Page 2 Question 1. 1. (TCO E) Ten Dodge Caravans were randomly selected from the classified ads. The following data gives the AGE (X, in years) and PRICE (Y, in $) for each of these 10 cars. AGE PRICE PREDICT 6 12500 4 6 11500 10 6 13000 2 26000 2 21900 5 15000 4 19000 5 16300 1 26000 4 16000 Correlations: AGE, PRICE Pearson correlation of AGE and PRICE = 0.968 PValue = 0.000 Regression Analysis: PRICE versus AGE The regression equation is PRICE = 29160 2790 AGE Predictor Coef SE Coef T P Constant 29160 1143 25.51 0.000 AGE 2790.3 256.3 10.89 0.000 S = 1424.65 RSq = 93.7% RSq(adj) = 92.9% Analysis of Variance Source DF SS MS F P Regression 1 240578913 240578913 118.53 0.000 Residual Error 8 16237087 2029636 Total 9 256816000 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 17999 451 (16958, 19040) (14553, 21445) 2 1257 1578 (2381, 4896) (3645, 6159)XX XX denotes a point that is an extreme outlier in the predictors. Values of Predictors for New Observations New Obs AGE 1 4.0 2 10.0 a. Analyze the above output to determine the regression equation. b. Find and interpret 1 in the context of this problem. c. Find and interpret the coefficient of determination (r-squared). d. Find and interpret coefficient of correlation. e. Does the data provide significant evidence (= .05) that age can be used to predict price? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret. f. Find the 95% confidence interval for mean price for all 4-year-old Caravans. Interpret this interval. g. Find the 95% prediction interval for the price of a 4-year-old Caravan. Interpret this interval. h. What can we say about the price of a 10-year-old Caravan? (Points : 48) a- The regression equation is PRICE = 29160 - 2790 AGE y = 29160 - 2790 X b-MS= 2029636 c- r-sq = 92.9 how much variation in the date that we are explaining r2 implies that only of the sample variation in number --- cases can be explained by using age in the straight-line model. Analysis of Variance d- 0.929 e- Since @ = .10 and P = 0.000 P<@ then we Reject H0 there is sufficient evidence, and we say that the slope is significant. f- 95% CI (16958, 19040) : we are 95% confident that the data mean for each unit change in the -X value is between the limits of the confidence level (16958, 19040) g. 95% PI (14553, 21445): is the prediction interval we say that we are 95% confident that for one more year there change is between the limits of the prediction interval h- we say that the slop s significant . -the slope of the line B1 for each unit increase in mean pore diameter , the mean is estimated to increase by B1(the change in number as we add age Question 8 : Time Remaining: 00:37:16 Page: 1 2 3 Page 2 Question 1. 1. (TCO E) Ten Dodge Caravans were randomly selected from the classified ads. The following data gives the AGE (X, in years) and PRICE (Y, in $) for each of these 10 cars. AGE PRICE PREDICT 6 12500 4 6 11500 10 6 13000 2 26000 2 21900 5 15000 4 19000 5 16300 1 26000 4 16000 Correlations: AGE, PRICE Pearson correlation of AGE and PRICE = 0.968 PValue = 0.000 Regression Analysis: PRICE versus AGE The regression equation is PRICE = 29160 2790 AGE Predictor Coef SE Coef T P Constant 29160 1143 25.51 0.000 AGE 2790.3 256.3 10.89 0.000 S = 1424.65 RSq = 93.7% RSq(adj) = 92.9% Analysis of Variance Source DF SS MS F P Regression 1 240578913 240578913 118.53 0.000 Residual Error 8 16237087 2029636 Total 9 256816000 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 17999 451 (16958, 19040) (14553, 21445) 2 1257 1578 (2381, 4896) (3645, 6159)XX XX denotes a point that is an extreme outlier in the predictors. Values of Predictors for New Observations New Obs AGE 1 4.0 2 10.0 a. Analyze the above output to determine the regression equation. b. Find and interpret 1 in the context of this problem. c. Find and interpret the coefficient of determination (r-squared). d. Find and interpret coefficient of correlation. e. Does the data provide significant evidence (= .05) that age can be used to predict price? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret. f. Find the 95% confidence interval for mean price for all 4-year-old Caravans. Interpret this interval. g. Find the 95% prediction interval for the price of a 4-year-old Caravan. Interpret this interval. h. What can we say about the price of a 10-year-old Caravan? (Points : 48) aThe regression equation is PRICE = 29160 - 2790 AGE y = 29160 - 2790 X b-MS= 2029636 c- r-sq = 92.9 how much variation in the date that w e are explaining r2 implies that only of the sample variation in number --- cases can be explained by using age in the straight-line model. Analysis of Variance d- 0.929 e- Since @ = .10 and P = 0.000 P<@ then w e Reject H0 there is The regression equation is Perceived_Recovery = 3.24 + 2.53 Blood_Lactate_Level ___ > y = 3.24 + 2.53 X 1-the slope of the line B1 for each unit increase in mean pore diameter , the mean is estimated to increase by B1(the change in number of --- as we add one factor ---X-- .) Predictor Coef SE Coef T P Constant 3.244 5.332 0.61 0.553 Blood_Lactate_Level 2.533 1.055 2.40 0.031 S = 4.53825 R-Sq = 29.2% R-Sq(adj) = 24.1% 2-R-Sq(adj) = 24.1% : how much variation in the date that we are explaining r2 implies that only 24.3% of the sample variation in number --- cases can be explained by using ----(x) in the straight-line model. Analysis of Variance Source DF SS MS F P 1 118.66 118.66 5.76 0.031 Residual Error 14 288.34 20.60 Total 15 407.00 Regression 3-confidenece level : New Obs Fit SE Fit 1 33553 5201 95% CI (21559, 45548) 95% PI (21227, 45880)XX a- 95% PI : is the prediction interval we say that we are 95% confident that the actual ---- accuracy ...... for each unit X change --- is between the limits of the prediction interval b- 95% CI : we are 95% confident that the mean of ...... for each unit change in the -X value -- is between the limits of the confidence level (22.22,33.3) . 4-Since @ = .10 and P = 0.031 P<@ then we Reject H0 there is sufficient evidence, and we say that the slope is significant. To find P-Value we go : Stat > Basic stat > correlation > choose display P-value Q8 : Y = -1339 + 86 numberID + 12.3 Age Find P > H0: b2 = 0 Ha: b2 0 Find T> H0: b1 =0 Ha: b1 0 R-Sq(adj)= 66% Means that the varation of price can be explained by the variation of the number of - and of --- PRICE = - 1339 + 12.7 AGE + 86.0 NUMBIDS For each one year increase of the --- age the price increases in average of 12.7 if we assumed that the number of piders is constant . 12.7 AGE : For each one increase of the --- piders numberthe price increases in average of 86 if we assumed that the number of Age is constant . 86.0 NUMBIDS: Q8: a. a. Ho: u = .500 Ha: p u <500 b. significance level is alpha .10 c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. z<-1.28 d. Z = -1.17 One-Sample Z Test of mu = 500 vs < 500 The assumed standard deviation = 84 90% Upper N Mean SE Mean Bound Z P 49 486.0 12.0 501.4 -1.17 0.122 e. Donot reject Ho f. This means that there's insufficent evidence to conclude the mean annual cdental expense. g. P value is 0.122 that means P>alpha we have .122> .10 that means don't reject Ho h. There 's insufficent evidence of sample data provide evidence (with a = 0.10), that the mean annual dental expense per employee is less than $500? \f\f\f\f\f\f\f\f\f