Business Finance
SYM506 GCU Buena School District Bus & Century National Bank Data Paper

Sym506

Grand Canyon University

Question Description

Complete the problems below from the textbook. You will need to use the "Buena School District Bus Data" and the "Century National Bank Data" files for this assignment.

  1. Chapter 8 – Problem 44
  2. Chapter 8 – Problem 48
  3. Chapter 9 – Problem 56
  4. Chapter 9 – Problem 66
  5. Chapter 9 – Problem 71
  6. Chapter 9 Case A – Century National Bank

For problems requiring computations, please ensure that your Excel file includes the associated cell computations and/or statistics output. This information is needed in order to receive full credit on these problems.

Submit output in one Excel file.

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44. An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.50 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute the mean price for the sample. a. What is the standard error of the mean in this experiment? b. What is the probability that the sample mean is between $3.46 and $3.54? c. What is the probability that the difference between the sample mean and the population mean is less than $0.01? d. What is the likelihood the sample mean is greater than $3.60? 48. Refer to the Buena School District bus data. Information provided by manufacturers of school buses suggests the mean maintenance cost per month is $455 per bus. Use statistical software to find the mean and the standard deviation for the Buena buses. Does the Buena data seem to be in line with that reported by the manufacturer? Specifically, what is the probability of the sample mean being less than Buena’s, given the manufacturer’s data? CH.9 55. You are to conduct a sample survey to determine the mean family income in a rural area of central Florida. The question is, how many families should be sampled? In a pilot sample of 10 families, the standard deviation of the sample was $500. The sponsor of the survey wants you to use the 95% confidence level. The estimate is to be within $100. How many families should be interviewed? 66. Near the time of an election, a cable news service performs an opinion poll of 1,000 probable voters. It shows that the Republican contender has an advantage of 52% to 48%. a. Develop a 95% confidence interval for the proportion favoring the Republican candidate. b. Estimate the probability that the Democratic candidate is actually leading. 71. Refer to the Buena School District bus data. a. Develop a 95% confidence interval for the mean bus maintenance. b. Develop a 95% confidence interval for the mean bus miles. c. Write a business memo to the state transportation official to report your results. Century National Bank Refer to the description of Century National Bank at the end of the Review of Chapters 1–4 on page 125. When Mr. Selig took over as president of Century several years ago, the use of debit cards was just beginning. He would like an update on the use of these cards. Develop a 95% confidence interval for the proportion of customers using these cards. On the basis of the confidence interval, is it reasonable to conclude that more than half of the customers use a debit card? Write a brief report interpreting the results Frequency Distribution - Quantitative Maintenance lower 320 340 360 380 400 420 440 460 480 500 520 540 560 Histogram 20 18 16 Percent 14 12 10 8 6 4 2 0 Maintenance Descriptive statistics count mean sample variance sample standard deviation minimum maximum range Maintenance 80 450.29 2,882.18 53.69 329 570 241 upper < < < < < < < < < < < < < 340 360 380 400 420 440 460 480 500 520 540 560 580 midpoint 330 350 370 390 410 430 450 470 490 510 530 550 570 width 20 20 20 20 20 20 20 20 20 20 20 20 20 frequency 3 3 1 8 5 12 12 15 7 8 1 3 2 80 1st quartile median 3rd quartile interquartile range mode low extremes low outliers high outliers high extremes 420.00 456.00 489.75 69.75 329.00 0 0 0 0 Frequency Distribution - Quantitative Maintenance lower upper 300 350 400 450 500 550 < < < < < < 350 400 450 500 550 600 midpoint 325 375 425 475 525 575 width 50 50 50 50 50 50 frequency 3 12 22 29 11 3 80 midpoint 343 378 413 width 35 35 35 frequency 6 8 12 Histogram 40 35 Percent 30 25 20 15 10 5 0 Maintenance Frequency Distribution - Quantitative Maintenance lower 325 360 395 upper < < < 360 395 430 430 465 500 535 570 < < < < < Histogram 30 25 Percent 20 15 10 5 0 Maintenance Descriptive statistics count mean sample variance sample standard deviation minimum maximum range 1st quartile median 3rd quartile interquartile range mode low extremes low outliers high outliers high extremes Miles 80 827.53 1,188.20 34.47 741 908 167 806.00 827.00 851.50 45.50 815.00 0 0 0 0 BoxPlot 465 500 535 570 605 448 483 518 553 587 35 35 35 35 35 20 20 9 4 1 80 BoxPlot 1/28/2010 16:03.39 (1) 600 650 700 750 800 850 900 950 850 900 950 850 900 950 Miles Descriptive statistics count mean sample variance sample standard deviation minimum maximum range Miles 80 827.53 1,188.20 34.47 741 908 167 1st quartile median 3rd quartile interquartile range mode 806.00 827.00 851.50 45.50 815.00 low extremes low outliers high outliers high extremes 0 0 0 0 BoxPlot 1/28/2010 16:06.08 (1) 600 650 700 750 800 Miles DotPlot 1/28/2010 16:06.08 (1) 600 650 700 750 800 Miles Descriptive statistics count mean sample variance sample standard deviation minimum maximum range 1st quartile median 3rd quartile interquartile range mode Miles 80 830.11 1,779.85 42.19 741 1008 267 806.00 827.00 851.50 45.50 815.00 low extremes low outliers high outliers high extremes 0 0 1 1 BoxPlot 1/28/2010 16:08.20 (1) 600 700 800 900 1000 1100 1000 1100 Miles DotPlot 1/28/2010 16:08.20 (1) 600 700 800 900 Miles Correlation Matrix Maintenance Age Maintenance 1.000 .465 Age 1.000 Miles Miles .450 .522 1.000 80 sample size ± .220 critical value .05 (two-tail) ± .286 critical value .01 (two-tail) percent 3.8 3.8 1.3 10.0 6.3 15.0 15.0 18.8 8.8 10.0 1.3 3.8 2.5 100.0 cumulative frequency percent 3 3.8 6 7.5 7 8.8 15 18.8 20 25.0 32 40.0 44 55.0 59 73.8 66 82.5 74 92.5 75 93.8 78 97.5 80 100.0 percent 3.8 15.0 27.5 36.3 13.8 3.8 100.0 percent 7.5 10.0 15.0 cumulative frequency percent 3 3.8 15 18.8 37 46.3 66 82.5 77 96.3 80 100.0 cumulative frequency percent 6 7.5 14 17.5 26 32.5 25.0 25.0 11.3 5.0 1.3 100.0 46 66 75 79 80 57.5 82.5 93.8 98.8 100.0 Data Set 3 --Buena School District Bus Data Bus Number X1 Maintenance X2 Age X3 Miles X4 Type X5 Bus-Mfg X6 Passenger X7 135 120 200 40 427 759 10 880 481 387 326 861 122 156 887 686 490 370 464 875 883 57 482 704 989 731 75 162 732 751 600 948 358 833 692 61 9 314 396 365 329 503 505 466 359 546 427 474 382 422 433 474 558 561 357 329 497 459 355 489 436 455 514 503 380 432 478 406 471 444 493 452 461 496 469 442 414 459 457 462 7 10 10 10 7 8 5 9 3 8 9 10 10 12 8 3 10 8 3 9 2 7 11 8 9 6 6 3 9 2 10 9 6 8 8 9 4 11 2 6 853 883 822 865 751 870 780 857 818 869 848 845 885 838 760 741 859 826 806 858 785 828 980 857 803 819 821 798 815 757 1008 831 849 839 812 809 864 859 815 799 Diesel Diesel Diesel Gasoline Gasoline Diesel Gasoline Gasoline Gasoline Gasoline Diesel Gasoline Gasoline Diesel Diesel Diesel Gasoline 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Final Answer

Hi,Find attached the completed work.Feel free to ask for any clarification or editing if need be.Looking forward to working with you in future.Thank you.

Running head: BUSINESS STATISTICS PROBLEMS

Business Statistics Problems
Student’s Name
Professor’s Name
Course Title
Date

BUSINESS STATISTICS PROBLEMS
44. An economist uses the price of a gallon of milk as a measure of inflation. She finds that
the average price is $3.50 per gallon and the population standard deviation is $0.33. You
decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute
the mean price for the sample.
a. What is the standard error of the mean in this experiment?
Standard error = δ / √n
0.33/√40 = 0.052178
b. What is the probability that the sample mean is between $3.46 and $3.54?
µ = 3.50
δ = 0.33
x1 = 3.46
x2 = 3.54
Z = (xi - µ)/δ
Z3.46 = (3.46 – 3.50)/0.33 = -0.1212
Z3.54 = (3.54 – 3.50)/0.33 = 0.1212
P (3.46 ≤ x ≤ 3.54) = P(-0.1212 ≤ Z ≤ 0.1212)
0.0478 + 0.0478 = 0.0956
P = 9.56%
It is very unlikely that a sample mean is between $3.46 and $3.54.
c. What is the probability that the difference between the sample mean and the population
mean is less than $0.01?

2

BUSINESS STATISTICS PROBLEMS
P (xs – xp) ˂ 1
P(x-bar > 3.08) = P(z > 2.8070) = normalcdf(2.8070,100) = 0.0025
d. What is the likelihood the sample mean is greater than $3.60?
Z = (3.60 – 3.50)/0.33 = 0.3030
P (x ≥ 3.60) = P (Z ≥ 0.3030)
0.5 -0.6179 = - 0.1179
= 11.79%
48. Refer to the Buena School District bus data. Information provided by manufacturers of
school buses suggests the mean maintenance cost per month is $455 per bus. Use statistical
software to find the mean and the standard deviation for the Buena buses. Does the
Buena data seem to be in line with that reported by the manufacturer? Specifically, what is
the probability of the sample mean being less than Buena’s, given the manufacturer’s data?

The calculated sample mean maintenance cost per month of the Buena buses is $450.29 while
the standard deviation is $53.69.
According to the information provided by the manufacturer, the mean maintenance cost per
month is $455 per bus.

3

BUSINESS STATISTICS PROBLEMS

4

The Buena data is in line with that reported by the manufacturer given that it falls within the 95%
confidence interval: 438.52 ≤ x ≤ 462.05
Z = (455 – 450.29)/53.69 = 0.0877
P (x ≤ 455) = P (Z ≤ 0.0877)
0.5 – 0.5359 = - 0.0359
= 0.4641
P = 46%
CH.9
55. You are to conduct a sample survey to determine the mean fami...

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