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Q1. Most air travellers now use e-tickets. Electronic ticketing…
Q1. Most air travellers now use e-tickets. Electronic ticketing allows passengers to not worry about a paper ticket, and it costs the airline companies less than paper ticketing. However, recently the airlines have received complaints from passengers regarding their e-tickets, particularly when connecting flights and a change of airlines were involved. To investigate the problem, an independent watchdog agency contacted a random Sample of 20 airports and collected information on the number of complaints the airport had with e-tickets for the month of March. The information is reported below.
14 14 16 12 12 14 13 16 15 14
12 15 15 14 13 13 12 13 10 12
At the .05 significance level, can the watchdog agency conclude the mean number of complaints per airport is less than 15 per month?
What steps should the researcher take to test the claim, give reasoning?
Test the claim at 5% level of significance.
Is the researcher, right? Explain it graphically.
What is a difference between Type I and Type II errors? Explain in respect to the above question.
Q1 The price of shares of Bank of Florida at the end of trading each day for the last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $42.00 per share and the standard deviation was $2.25 per share.
What is the probability that the end-of-day trading price is over $45.00?
Estimate the number of days in a year when the trading price finished above $45.00.
c. What is the minimum share price for the top 15% of end-of-day trading prices?
Q2. Excel was used to analyse the juice content in tetra packs at a packaging plant in India. A lab randomly samples 150 bottles and tests the bottles for fill volume. The descriptive statistics is given below. Write a brief report to supervisors summarizing what this output is saying about the process.
Tetra packs
Mean 20.00817
Standard error 0.0082781
Median 19.99697
Mode #NA
Standard deviation 0.101388
Kurtosis -0.11422
Skewness 0.080425
Range 0.557666
Minimum 19.7055
Maximum 20.26322
Sum 3001.225
Count 160
Q3. A recent article in Bloomberg Businessweek listed the “Best Small Companies.” We are interested in the current results of the companies’ sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below:
Company Sales ($million) Earnings ($million)
Papa John’s International $89.2 $4.9
Checkmate Electronics 17.5 2.6
Applied Innovation 18.6 4.4
IntegraCare 18.2 1.3
Wall Data 71.7 8.0
Davidson & Associates 58.6 6.6
Chico’s FAS 46.8 4.1
Royal Grip 11.9 1.7
M-Wave 19.6 3.5
Serving-N-Slide 51.2 8.2
Daig 28.6 6.0
Cobra Golf 69.2 12.8
Determine the regression equation.
For a small company with $50.0 million in sales, estimate the earnings.
Q4. Construct a box-and-whisker plot for the age of internet users obtained from a sample. Does the data contain any outliers? Comment on the plot and what inference can a researcher draw from the same?
4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.7, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4
Q5. The U.S. Postal Service reports 95% of first-class mail within the same city is delivered within 2 days of the time of mailing. Six letters are randomly sent to different locations.
a. What is the probability that all six arrive within 2 days?
b. What is the probability that exactly five arrive within 2 days?
c. Find the mean number of letters that will arrive within 2 days.
Q6. A certain disease has an incidence rate of 2%. If the false negative rate is 10% and the false positive rate is 1%, compute the probability that a person who tests positive actually has the disease.
Q7. The personnel files of all eight employees at the Pawnee location of Acme Carpet Cleaners Inc. revealed that during the last 6-month period they lost the following number of days due to illness:
2 0 6 3 10 4 1 2
All eight employees during the same period at the Chickpee location of Acme Carpet Cleaners revealed they lost the following number of days due to illness:
2 0 1 0 5 0 1 0
As the director of human resources, compare the two locations. What would you recommend?
Coeff of variation
Q1 The GMAT scores of students who are potential applicants to a business school are normally distributed with a mean of 650 and a standard deviation of 98.
What percentage of students will have scores exceeding 600?
If the business school wants only the top 75% of the students to be eligible to apply, what should be the minimum GMAT score specified for eligibility?
Q2. Below you are given a partial computer output based on a sample of 12 observations relating the number of personal computers sold by a computer shop per month (Y), unit price (X1 in $1,000) and the number of advertising spots (X2) used on a local television station.
Coefficient Standard Error t value P value
Constant 17.145 7.865
X1 -0.104 3.282 -0.032 0.2203
X2 1.376 0.250 5.505 0.0093
Use the output shown above and write an equation that can be used to predict the monthly sales of computers.
If the company charges $2,000 for each computer and uses 10 advertising spots, how many computers would you expect them to sell?
Q3. A manufacturing firm receives shipments of parts from two different suppliers. Currently, 65% of the purchased by the company are from supplier 1 parts and the remaining 35% are from supplier 2. 98% of parts received from supplier 1 are good where as 95% received from supplier 2 are good. What is the probability of randomly choosing a part which is bad and it belongs to supplier 1?
Q4. A research firm conducted a survey of 49 randomly selected Americans to determine the mean amount spent on coffee during a week. The sample mean was $20 per week. The population distribution is normal with a standard deviation of $5.
Using the 95% level of confidence, determine the confidence interval for the population mean µ. Explain what it indicates.
Base theorem
Q5. The McFarland Insurance Company Claims Department reports the mean cost to process a claim is $60. An industry comparison showed this amount to be larger than most other insurance companies, so the company instituted cost-cutting measures. To evaluate the effect of the cost-cutting measures, the supervisor of the Claims Department selected a random sample of 26 claims processed last month and recorded the cost to process each claim. The sample information is reported below.
$45 $49 $62 $40 $43 $61
48 53 67 63 78 64
48 54 51 56 63 69
58 51 58 59 56 57
38 76
At the .01 significance level, is it reasonable to conclude that the mean cost to process a claim is now less than $60?
Q6. The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes).
Quarter-Mile Times: 0.92 0.98 1.04 0.90 0.99
Mile Times: 4.52 4.35 4.60 4.70 4.50
After viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent times. Is he correct? Give explanation.
Coeff Of variatin
Q7. For its Music 360 survey, Nielsen Co. asked teenagers and adults how each group has listened to music in the past 12 months. Nearly two-thirds of U.S. teenagers under the age of 18 say they use Google Inc.’s video-sharing site to listen to music and 35% of the teenagers said they use Pandora Media Inc.’s custom online radio service (The Wall Street Journal). Suppose 10 teenagers are selected randomly to be interviewed about how they listen to music.
What is the probability that none of the 10 teenagers uses Pandora Media Inc.’s online radio service?
What is the probability that at least 2 of the 10 teenagers use Pandora Media Inc.’s online radio service?
Binominal distribution
