Question

SUBJECT : Quantitative Techniques (MBA)

Question 1

The Inland Revenue Board says that the average income in Taiping is RM15000. A sample of 45 people found that their mean income to be RM14300 with a standard deviation of RM2000. (a) Use a 5% significance level to check the claim. [18 marks]

(b) Test the effect of using a 1% significance level. [8 marks]

(c) If there is a difference in the two test results, explain the reason for the difference. [6 marks]

Question 2

A delivery company charges customers a flat rate for delivery based on a mean weight for packages of 1.75 kg with a standard deviation of 0.5 kg. Postage costs have risen and it seems likely that the mean weight is greater than 1.75 kg. The company checked a random sample of 100 packages and found a mean weight of 1.86 kg. Test the notion that the mean weight is more than 1.75 kg. [18 marks]

Question 3

You are a management consultant who has recently introduced a new procedure to a reception office. The receptionist should do at least 10 minutes of paperwork in each hour. You made a check on 40 random hours of work and found that the mean time spent on paperwork is 8.95 minutes with a standard deviation of 3 minutes. Test to see if the new procedure meets specifications at a 1% level of significance. [18 marks]

Answer #1

18. The average loan debt for college seniors is $20,262. If the
debt is normally distributed with a standard deviation of $5100,
find these probabilities: (3 points each)
Find the probability that a randomly selected senior owes at
least $21,000.
Find the probability that the mean debt from a sample of 20
seniors falls between $20,000 and $21,000.
(3 points) The average weight of a package of rolled oats is
supposed to be at least 18 ounces. A sample of...

1) A sample of 143 households yielded
an average income of $1500 per month with a standard deviation of
$514. The researcher wants to test at the 10% level of significance
that the average monthly income of all households is not greater
than $1575. What is the alternative hypothesis of this test?
Select one:
a. Mean = $1575
b. Mean > $1575
c. Mean < $1575
d. Mean ≠ 1575
2) Last year a sample of 164 farmers had an...

QUESTION 1
Joyce works in a toy factory maintaining machines. Machines
should inject exactly 500 grams of plastic into a mold to make a
toy plane. Joyce wonders if these toy machines might need cleaning,
but it's a lot of work taking apart the machines to do a proper
job. She grabs planes from 24 different machines at random and
weighs them. Her average is 495 grams. She knows there's a standard
devation of 10 grams for all machines (Joyce...

Question 1
The production manager of a camera manufacturer claims that
their
latest digital camera is able to focus in just 0.0025 seconds on
the
average. A random sample of the focus time in seconds for 20
cameras
is collected and the times are recorded as follows:
0.0033
0.0028
0.0021
0.0032
0.0020
0.0025
0.0026
0.0022
0.0031
0.0033
0.0022
0.0025
0.0031
0.0024
0.0021
0.0023
0.0028
0.0031
0.0028
0.0035
a) In constructing a confidence interval estimate for the true
average
focus time,...

A video producer wants to determine whether the 2 types of
microelectric circuits it uses have the same flow rates. The
research engineer has obtained the following data. Interpret the
result at a 10% significance level. (Assuming the variances are not
equal.)
.
First design
Second Desingn
Sample mean(X)
24.2
23.9
Sample
standard derivation(S)
3.16
4.47
Number of observations(n)
15
12
b) A substance is used to increase the reaction rate at a
chemical concentration. When the amount of this...

Question 1 (1 point)
Suppose the national average dollar amount for an automobile
insurance claim is $746.9. You work for an agency in Michigan and
you are interested in whether or not the state average is different
from the national average. Treating the national mean as the
historical value, What are the appropriate hypotheses for this
test?
Question 1 options:
1)
HO: μ ≤ 746.9
HA: μ > 746.9
2)
HO: μ > 746.9
HA: μ ≤ 746.9
3)
HO:...

Question 1)
College basketball, and particularly the NCAA basketball
tournament, is a popular venue for gambling, from novices in office
betting pools to high rollers. To encourage uniform betting across
teams, Las Vegas oddsmakers assign a point spread to each game. The
point spread is the oddsmakers’ prediction for the number of points
by which the favored team will win. If you bet on the favorite, you
win the bet provided the favorite wins by more than the point
spread;...

Question 1 (1 point)
Saved
It is reported in USA Today that the average flight cost
nationwide is $327.31. You have never paid close to that amount and
you want to perform a hypothesis test that the true average is
actually different from $327.31. What are the appropriate
hypotheses for this test?
Question 1 options:
1)
HO: μ ≤ 327.31
HA: μ > 327.31
2)
HO: μ ≥ 327.31
HA: μ < 327.31
3)
HO: μ ≠ 327.31
HA: μ...

Joyce works in a toy factory maintaining machines. Machines
should inject exactly 500 grams of plastic into a mold to make a
toy plane. Joyce wonders if these toy machines might need cleaning,
but it's a lot of work taking apart the machines to do a proper
job. She grabs planes from 24 different machines at random and
weighs them. Her average is 495 grams. She knows there's a standard
devation of 10 grams for all machines (Joyce has been...

QUESTION 1
In order to compare the mean length of advertising breaks of
two Irish TV networks: the mean length of breaks on network 1, μ
1, and the mean length of breaks on network 2, μ
2, independent random samples of ad-breaks are selected
from each network, and their lengths measured in minutes.
Descriptive statistics found for each sample of TV ad-breaks are
provided in the table below :
Group Statistics
GROUP
n
Mean
Std. Deviation
AdbreakLength
network 1...

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