EPGP 13 – Quantitatve Techniques
Sample Quiz 3
Sec C&D
Instructor: Sandip Barui
Retail Store Case Study:
From an areawide survey 6 months back on a retail store chain X (with 18 stores operating in the area), it’s
found that any standard store makes a mean daily profit of Rs.1.8 lacs. A new marketing campaign
(Campaign A) has been launched a month back which focuses on selling few selected essential household
items at 75% of the original price. An area sales supervisor wants to know if the mean daily profit for a store
in the area has increased significantly because of this campaign. So, he instructed store managers at two
local stores to collect daily sales data from their stores for the last 10 days. From the data obtained from
these managers, the area sales supervisor observed that the mean daily profit value is Rs. 2.1 lacs with
SD of Rs. 0.55 lacs based on 20 sample observations (corresponding to two stores and 10 days). It may
be assumed that the daily profit values are normally distributed.
Use information given above to answer the following questions 1 – 15.
1.
What should be considered as the target population of the study?
a. Daily profit values from all retail stores in the country under chain X
b. Daily profit values from all 18 retail stores in the area under chain X
c. Daily profit values from only the two retail stores in the area
d. Daily profit values for the last 10 days obtained from the two retail stores in the area
2. What is the sample considered for the study?
a. Daily profit values from all retail stores in the country under chain X
b. Daily profit values from all 18 retail stores in the area under chain X
c. Daily profit values from only the two retail stores in the area
d. Daily profit values for the last 10 days obtained from the two retail stores in the area
3. What is the parameter of interest for the study?
a. Mean daily profit value for a store based on all retail stores in the country under chain X
b. The observed mean daily profit value of Rs. 2.1 lacs based on 20 samples observations
obtained from the two retail stores
c. The proportion of days when mean daily profit for a store is greater than Rs. 1.8 lacs
d. Mean daily profit value for a store based on all 18 retail stores in the area under chain X
4.
What is a reasonable statistic in this case? Is statistic a random variable?
a. Sample mean �� where the sample comprises daily profit values from the two retail
stores in the area for the last 10 days. It’s a random variable.
b. Sample mean �� where the sample comprises daily profit values from all 18 retail stores
in the area under chain X.
c. Sample proportion ��̂ where the sample comprises daily profit values from the two retail
stores in the area for the last 10 days. It’s a random variable.
d. Sample mean �� where the sample comprises daily profit values from the two retail
stores in the area for the last 10 days. It’s NOT a random variable.
5.
What is the main statistical objective of the study?
a. To find out or estimate the value of the population mean, i.e., the mean daily profit value
for a store based on all 18 retail stores (under chain X) in the area after the marketing
campaign
b. To test (statistically) whether the mean daily profit value for a store based on all 18 retail
stores (under chain X) in the area has increased significantly after the marketing campaign
c. To find out or estimate the value of the population mean, i.e., the mean daily profit value
for a store based on all retail stores (under chain X) in the country after the marketing
campaign
d. To test (statistically) whether the mean daily profit value for a store based on the 20 sample
data from the two retail stores (under chain X) in the area has increased significantly after
the marketing campaign
6.
What is a point estimate of the parameter of interest?
a. The value of the sample mean daily profit for a store based on the two retail stores in the
area, i.e., Rs. 1.8 lacs based on the survey performed 6 months back.
b. The value of the population mean daily profit for a store based on the 18 retail stores in the
area, i.e., Rs. 1.8 lacs based on the survey performed 6 months back.
c. The value of the sample mean daily profit for a store based on the 2 retail stores in the
area, i.e., Rs. 2.1 lacs based on the last 10 days daily profit values.
d. A point estimate can’t be comprehensively measured in this case due to the lack of
sufficient information.
7.
Which of the following is also a statistic to estimate the parameter of interest?
a. Geometric Mean = �����1��2 … ���� of the sample
b. Harmonic mean = �� �
1
+
�
�2
��1
c.
1
Trimmed Arithmetic Mean =
+⋯ +
1 −1
�
of the sample
����
����+1 +⋯ +����+�
��
of the sample for any 0 ≤ �� ≤ �� − �� and 1 ≤ �� ≤
�� − 1
d. All of the above
8.
Which of the following is an appropriate 95% confidence interval for the parameter of interest?
�� × �
�� × � � = (1.842, 2.357).
a. �� − ��
� , �� +
�
��−1; 2
��
b. �� − �� ��;�� ×
2
c.
×
��� − ����
2
√�
�
��
√�
�
√�
�
��−1; 2
��
��
, �� +
��
��;
��
×
2
��
√�
�
√�
�
� = (1.843, 2.356).
, �� + ���� � = (1.859, 2.341).
√�
×
�
2
d. None of the above.
9. For what value of ��, the area under the curve greater than �� for a t-distribution with d.f. 19 is 0.05?
a. T.INV(0.05,19)
b. T.INV(0.95,19)
c. T.DIST(0.05,19)
d. T.INV(0.05,18)
10. Why is the assumption of normality required in this case?
a. This assumption is redundant and doesn’t have any impact on sampling distribution of the
��−��
statistic �
�.
��/√��
b. If the population values are not normal with unknown SD and the sample size is small, then
��−��
the sampling distribution of the statistic �
� follows normal distribution.
��/√��
c.
If the population values are normal with unknown SD and the sample size is small, then
��−��
the sampling distribution of the statistic �
� doesn’t follow t-distribution, and has to
��/√��
evaluated case by case basis.
d. If the population values are not normal with unknown SD and the sample size is small, then
��−��
the sampling distribution of the statistic �
� doesn’t follow t-distribution or any known
��/√��
distribution, and has to evaluated case by case basis.
11. What would be a meaningful test of hypothesis for this study?
a. �0: �� = 1.8 vs. ��0: �� ≠ 1.8 where �� is the population mean
b. �0: �� = 1.8 vs. ��0: �� = 2.1 where �� is the population mean
c. ��0: �� = 1.8 vs. ��0: �� > 1.8 where �� is the population mean
d. �0: �� = 2.1 vs. ��0: �� > 2.1 where �� is the population mean
12. The critical value for the correct test in this case is 1.7291 for a significance level of 5%. This means:
a. The area under the curve for values greater than 1.7291 of the sampling distribution is 5%.
b. The area under the curve for values lesser than 1.7291 of the sampling distribution is 5%.
c. The area under the curve for values greater than 1.7291 and lesser than -1.7291 of the
sampling distribution is 5%.
d. The area under the curve for values lying in between -1.7291 and 1.7291 of the sampling
distribution is 5%.
13. The test statistic value is 2.4393. What would you infer?
a. Since the test statistic value 2.4393 is greater than the critical value 1.7291, we fail to reject
the null hypothesis at 5% level implying that the marketing campaign was indeed NOT
effective in increasing the mean daily profit for a store in the area significantly.
b. Since the test statistic value 2.4393 is greater than the critical value 1.7291, we reject the
null hypothesis at 5% level implying that the marketing campaign was indeed NOT effective
in increasing the mean daily profit for a store in the area significantly.
c. Since the test statistic value 2.4393 is greater than the critical value 1.7291, we reject the
null hypothesis at 5% level implying that the marketing campaign was indeed effective in
changing the mean daily profit for a store in the area significantly.
d. Nothing can be inferred since the p-value of the test is not given.
14. The p-value is 0.012. This means:
a. The area under the curve for values lesser than 2.4393 of the sampling distribution is 1.2%.
b. The area under the curve for values greater than 2.4393 of the sampling distribution is
1.2%.
c. The combined area under the curve for values lesser than -2.4393 and greater than 2.4393
of the sampling distribution is 1.2%.
d. The area under the curve for values greater than 1.7291 of the sampling distribution is
1.2%.
15. If the study is to test whether the marketing campaign has indeed any effect on the mean daily
profit for a store, how would the p-value change?
a. p-value would be 0.024
b. p-value would be 0.006
c. p-value would remain same, i.e., 0.012
d. p-value would be 1
Based on Example 10.3 from the text book: An insurance company’s procedure in settling a claim under
$10000 for fire and water damage is to require two estimates for clean up and repair of structural damage
before allowing the insured to proceed with the work. The insurance company compares estimates from
two contractors who frequently handle this type of work in this geographical area. At 0.05 level of
significance, is there a difference between the two contractors? The Excel output for the analysis is given
below in Table 1. Based on the output please answer questions 16 – 19:
t-Test: Paired Two Sample for
Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Contractor A Contractor
B
4690
4930
7836555.556 9053444.44
4
10
10
0.996247386
0
9
-2.318963855
0.022781515
1.833112933
0.04556303
2.262157163
16. What is the p-value of the test and what does it mean?
a. The p-value is 0.0227; it means there is sufficient evidence to reject the null hypothesis in
favor of the claim that there is a significant difference between the two contractors at 5%
level.
b. The p-value is 0.0455; it means there isn’t enough evidence to reject the null hypothesis in
favor of the claim that there is a significant difference between the two contractors at 5%
level.
c. The p-value is 0.0455; it means there is sufficient evidence to reject the null hypothesis in
favor of the claim that there is a significant difference between the two contractors at 5%
level.
d. The p-value is 2.2621; it means there isn’t enough evidence to reject the null hypothesis in
favor of the claim that there is a significant difference between the two contractors at 5%
level.
17. What kind of samples are these and which test is the most appropriate?
a. The samples are dependent; t-test: Paired Two Sample for Means
b. The samples are independent; t-test: Paired Two Sample for Means
c. The samples are dependent; t-test: Two-Sample Assuming Unequal Variances
d. The samples are independent; z-test: Two Sample for Means
18. What is/are the critical value/s for the test?
a. 2.2622
b. 1.8331
c. 0 and 2.2622
d. -2.2622 and 2.2622
19. What is/are the rejection region/s for the test?
a.
b.
c.
d.
Greater than 2.2622
Less than 2.2622
Greater than 2.2622 and less than -2.2622
Greater than -2.2622
20. What is true about a 95% confidence interval (CI)?
a. The probability of the true parameter lying inside the interval is 0.95.
b. CIs are random; out of 100 such random CIs we can expect approximately 95 of those to
contain the true parameter value.
c. CIs are random; out of 100 such random CIs exactly 95 of those would contain the true
parameter value.
d. CIs are random; out of 100 such random CIs we can expect approximately 95 of those to
contain the sample mean.
Answer Key (in order of the question numbers):
b, d, d, a, b, c, d, a, b, d, c, a, c, b, a, c, a, d, c, b