Without any endorsement, SKII’s average daily sales in Taipei are 500 units.
Sharon, the brand manager of SKII as well as a graduate of NTU MBA,
believes that promoting the product by favorable endorsers will increase the
amount of sales. She calculates that the improved sales by additional 75 units
daily would pay for the cost of the endorsement. Any further increase in sales
would create an extra profit. To test her belief that endorsers would lead to a
positive effect on profit, 田中千繪is invited to endorse SKII. Please answer the
following 6 questions (1-6).
To examine Sharon’s belief, the null hypothesis is
Without any endorsement, SKII’s average daily sales in Taipei are 500 units.
Sharon, the brand manager of SKII as well as a graduate of NTU MBA,
believes that promoting the product by favorable endorsers will increase the
amount of sales. She calculates that the improved sales by additional 75 units
daily would pay for the cost of the endorsement. Any further increase in sales
would create an extra profit. To test her belief that endorsers would lead to a
positive effect on profit, 田中千繪is invited to endorse SKII. Please answer the
following 6 questions (1-6).
If the cost of endorsement is not considered high in relation to
administrative expenses, and Procter & Gamble is eager to raise the profit
margin in Asia market, which of the following can best be used as the
significance level set by Sharon?
.01
.05
.10
depending on target customers’ buying behaviors
Without any endorsement, SKII’s average daily sales in Taipei are 500 units.
Sharon, the brand manager of SKII as well as a graduate of NTU MBA,
believes that promoting the product by favorable endorsers will increase the
amount of sales. She calculates that the improved sales by additional 75 units
daily would pay for the cost of the endorsement. Any further increase in sales
would create an extra profit. To test her belief that endorsers would lead to a
positive effect on profit, 田中千繪is invited to endorse SKII. Please answer the
following 6 questions (1-6).
If the average daily sales approaches 550 units after 田中千繪 serves as
the endorser, then which alternative hypothesis should Sharon use to test
her belief?
Without any endorsement, SKII’s average daily sales in Taipei are 500 units.
Sharon, the brand manager of SKII as well as a graduate of NTU MBA,
believes that promoting the product by favorable endorsers will increase the
amount of sales. She calculates that the improved sales by additional 75 units
daily would pay for the cost of the endorsement. Any further increase in sales
would create an extra profit. To test her belief that endorsers would lead to a
positive effect on profit, 田中千繪is invited to endorse SKII. Please answer the
following 6 questions (1-6).
.25
.75
.05
Unknown
Without any endorsement, SKII’s average daily sales in Taipei are 500 units.
Sharon, the brand manager of SKII as well as a graduate of NTU MBA,
believes that promoting the product by favorable endorsers will increase the
amount of sales. She calculates that the improved sales by additional 75 units
daily would pay for the cost of the endorsement. Any further increase in sales
would create an extra profit. To test her belief that endorsers would lead to a
positive effect on profit, 田中千繪is invited to endorse SKII. Please answer the
following 6 questions (1-6).
The probability of rejecting the null hypothesis when it is false is .04.
The probability of rejecting the null hypothesis when it is true is .04.
The probability of not rejecting the null hypothesis when it is true
is .95.
None of the above
Without any endorsement, SKII’s average daily sales in Taipei are 500 units.
Sharon, the brand manager of SKII as well as a graduate of NTU MBA,
believes that promoting the product by favorable endorsers will increase the
amount of sales. She calculates that the improved sales by additional 75 units
daily would pay for the cost of the endorsement. Any further increase in sales
would create an extra profit. To test her belief that endorsers would lead to a
positive effect on profit, 田中千繪is invited to endorse SKII. Please answer the
following 6 questions (1-6).
.05
.015
.03
None of the above
Grant, a senior marketing supervisor in HP, have noticed for a long time
that there is a one-to-one correspondence between the number of
butterflies observed in his front yard and the number of complaints filed by
key accounts on any given day. For example, without exception, whenever
a complaint was received, Grant could only find one butterfly in the front
yard; whenever two complaints were received, Grant could only find two
butterflies in the front yard, and so on. Retrieving from the vague scenes
back to 20 years ago, Grant still remembers by what have been learned in
the statistics class that he could use Y = X to represent his observations,
where Y is the number of butterfly observed and X the number of
complaints received. Which of the following is correct?
The number of complaints received is the cause and the number of
butterfly observed is the effect.
The number of complaints received is the effect and the number of
butterfly observed is the cause.
The covariance between the number of complaints received and the
number of butterfly observed is positive.
Grant can also use the regression analysis and the coefficient of the
predictor would be 1.
Asus’s VP in strategy would like to evaluate the performance of customer
relationship management (CRM) in cellular phone division and
motherboard division. Three 9-point (−4 to 4) differential semantic scales
are used to measure customers’ perceptions on Asus’s cellular phones and
motherboards. The evaluation index is obtained by averaging three scales.
By collecting 300 responses from Asus’s cellular phone users, the mean
evaluation index is 2.8 and the standard error is 3.7. Another 250
responses from Asus’s motherboard customers reported a mean of 2.6 and
a standard error of 1.3 on the evaluation index. Which of the following
statements is CORRECT?
In order to get a more accurate result in analysis, it is better to
transform the bipolar scale (e.g., −4 to 4) to the unipolar scale (e.g., 1 to
9)
When the sample size is getting larger, the sample mean is more likely
to get closer to the population mean.
Asus’s VP in strategy should conclude that the performance of CRM in
cellular phone and motherboard divisions are doing equivalently well,
because according to the analysis of one-way ANOVA, the mean
difference is much smaller than the standard deviations.
Asus’s VP in strategy should conclude that the performance of CRM in
cellular phone and motherboard divisions are doing equivalently well,
because according to the analysis of one-way ANOVA, the treatment
mean square is much smaller than the error mean square.
Laura, the product manager, would like to use the regression analysis to
examine whether the design style may produce different sales volume. She
still remembers that dummy variables should be used in such a regression
analysis. How many dummy variables should Laura use in the regression
analysis?
3
4
5
None of the above
Which of the following statements is CORRECT?
In a two-way ANOVA, if the interaction is significant, either main
effect is not supposed to be significant.
In a two-way ANOVA, if the main effect of factor A is not significant,
the mean difference between A1 and A2 at the level of B1 can still be
significant.
In a two-way ANOVA, if the overall interaction effect is not significant,
the interaction of the ith level of factor A and jth level of factor B can
still be significantly different from zero.
In a one-way ANOVA, when all factor level means are equal, the
expected value of the treatment mean square should be smaller than
the expected value of the error mean square such that null hypothesis
will not be rejected.
Which of the following statement is CORRECT?
In a chi-square test of independence, if marital status is found
associated with employment status, then we can predict that the
number of unmarried persons who are unemployed is very close to the
number of unmarried persons who are unemployed.
When there is not a significant match between the observed and
expected values, the chi-square will be significant.
When the test of chi-square is not significant, the chi-square value can
sometimes be negative.
The distribution of chi-square is generally symmetric, just like a bell
shape. Therefore, statisticians sometimes use normal distributions to
approximate chi-square distributions.
Suppose that the number of minutes between successive arrivals of the
Taipei MRT train at a station is uniformly distributed on (0.1). Passengers
arrive according to a Poisson process with a rate λ . Suppose a train has
just left the station. Let X denote the number of people who get on the
next train. Find (5%)
(a) E(X)
(b) Var(X)
Data on the monthly service fee in dollars when a customers’ account falls
below the minimum required $5000 balance for a sample of 26 banks yields
a sample mean of 71.5 and a sample standard deviation of 30.55 (10%)
(a) Please find a 95% confidence interval for the population mean monthly
service fee.
(b) Can we say that with probability 0.95 the interval obtained in (a) will
include the population mean? If not, then what is the correct
interpretation? Explain briefly.
(c) Data on 10 more banks were added so that the sample size increase to
36 and we obtained a 95% confidence interval [59.55, 80.45]. What is
the mean of the sample of 36?
(d) Assume that the estimated population standard deviation in (c) equals
the true population s.d. What is the minimum sample size required so
that the length of the 95% interval is less than 16?
The output of a fully-functioning power plant has a Gaussian distribution,
with a mean of 10MW and a standard deviation of 0.5MW. Upper and
lower control limits are established as 11.0 MW and 9.0 MW respectively.
If a certain component fails, the mean output drops to 9.0 MW, without
changing the standard deviation. (7.5%)
(a) What is the probability that the output lies between the control limits,
when the power plant is working properly?
(b) What is the probability that the output lies between the control limits
during one of the partial failures?
(c) If the power plant works properly 99% of the time, what is the
probability that going outside the control limits means a component
has failed?
Suppose Var(X) = 49 and Var(Y ) = 9 . For what values of the correlation
of X and Y is the Var(.2X + .8Y ) less than Var(Y ) ? (2.5%)
In a study to investigate the effect of speed on accident severity, 5000
accident reports of fatal automobile accidents were examined, and the
vehicle speed at impact was recorded for each one. It was determined that
the average speed was 52 mph with a standard deviation of 15 mph. Using
Chebyshev’s Theorem, write a statement about vehicle speed in fatal
accidents. (5%)
Suppose that the following data represents serum cholesterol levels in
mg/dL of a sample of 16 people before and after they adopted a vegetarian
diet.
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