MG 620 Research and statistics for Managers Final Exam Instructions: Answer all questions Part I : Problem 1. Fitting a straight line to a set of

Construct a frequency distribution, using 4 classes and a class width of 2 hours, and a lower limit of 8 for class 1.

• An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 10 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals daily revenue of $625.

Consider H0:  µ = 675  versus  Ha:  µ < 675

At the .05 level of significance , is there evidence that the average daily revenue is less than 675Compute the p-value and interpret its meaningConstruct a 95% confidence interval estimate of the population mean revenue of coin-operated laundry.Compare the results of (a) , (b), and (c). What conclusions do you reach?State the HypothesisDraw the normal distribution and identify the acceptance and rejection regionsMake your decision with respect to each part of the question.

Part I : Problem

Fitting a straight line to a set of data yieldsthe following prediction line:

Interpret themeaning of the Y intercept, b0.

ii)Interpret the meaning of the slope, b1

iii)Predict the mean value of Y for X = 5

What is the differencebetween the standard deviation, standard error of the mean, and standard errorof the estimate? Discuss

The standard deviation measures the amount ofvariability or dispersion for a subject set of data from the mean, while thestandard error of the mean measures how far the sample mean of the date islikely to be from the true population mean. The standard error is an estimateof the standard deviation of a statistic. , it is used to compute theconfidence intervals and margins of error.

In a sample of size of 5, the sum of all values is 200.What is the sample mean

20                                      c.         800

40                                      d.         None of the above

SHOW YOUR WORK!

Time (in minutes)               Relative Frequency

0 but less than 5                                               0.37

            5 but less than 10                                 0.22

            10 but less than 15                               0.15

            15 but less than 20                               0.10

            20 but less than 25                               0.07

            25 but less than 30                               0.07

            30 or more                                           0.02

Referring to Table 1, whatis the width of each class?

1 minute                                  c.         5minutes

2%                                           d.         100%

SHOW YOUR WORK!

1.     Width refers to thedifference between the lower limit of any two consecutive classes

2.     Therefore, 5-0 = 5 or 10-5 =5

Referring to Table 1, whatis the cumulative relative frequency for the percentage of calls that lastedunder 10 minutes?

c.         0.59

d.         0.84

Cumulativerelative frequency is the sum of all relative frequency from the top to thelast values: for example, the sum of all calls under 10 minutes is found byadding (.37 + .22) = .59). for under 20 minutes, it is .84 as shown above forall values in the third column.

The managers of a real estate firm are interested infinding out if the number of new clients a broker brings into the firm affectsthe sales generated by the broker. They sample 5 brokers and determine thenumber of new clients they have enrolled in the last year and their salesamounts in thousands of dollars. These data are presented in the table thatfollows.

Broker            Clients            (X)       Sales (Y)

1                      1                      4

2                      6

1                      3

0                      1

1                      1