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STATISTICS (STAT-101)
(Pre-MBA)
Assignment No. 2 week9-week14
Student Full Name:___________________________________ .
Student ID:__________________________________________ .
CRN No:____________________________________________ .
Branch: _____________________________________________.
Total Marks
MCQ:----------------/30
Short Answer:---------------/12
Day: Tuesday
Date: 21.7.1438
Long Answer: --------------/18
Total :--------------/60
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STATISTICS (STAT-101) (Pre-MBA)
Answer all the Questions on the same question paper.
Marks- 60
Section-I
(Multiple Choice Questions)
1.
a.
b.
c.
d.
(30 marks, 1 Mark Each)
An assumption made about the value of a population parameter is called a
hypothesis
conclusion
confidence
Significance
2. In hypothesis testing, the tentative assumption about the population
parameter is
a. the alternative hypothesis.
b. the null hypothesis.
c. either the null or the alternative.
d. None of these alternatives is correct.
3.
a.
b.
c.
d.
What type of error occurs if you fail to reject H0 when, in fact, it is not true?
Type II
Type I
either Type I or Type II, depending on the level of significance
either Type I or Type II, depending on whether the test is one tail or two tail
4.
a.
b.
c.
d.
The p-value
is the same as the Z statistic.
measures the number of standard deviations from the mean.
is a distance.
is a probability.
5.
a.
b.
c.
d.
In hypothesis testing if the null hypothesis is rejected,
no conclusions can be drawn from the test.
the alternative hypothesis is true.
the data must have been accumulated incorrectly.
the sample size has been too small.
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6.
a.
b.
c.
d.
The level of significance
can be any positive value.
can be any value.
is (1 - confidence level).
can be any value between -1.96 to 1.96 .
7. The A hypothesis test for a population proportion p is given below:
H0: p = 0.10
Ha: p ≠ 0.10
Sample size n = 100 and sample proportion p̂ = 0.15. z-statistic = ?
a. 
b. 
c. 1.12
d. -1.12
8. The average monthly rent for one-bedroom apartments in Chattanooga has
been $700. Because of the downturn in the real estate market, it is
believed that there has been a decrease in the average rental. The correct
hypotheses to be tested are
a. H0:   700
Ha:  < 700
b. H0:  = 700
Ha:   700
c. H0:   700
Ha:  700
d. H0:  < 700
Ha:   700
9. A student believes that the average grade on the final examination in
statistics is at least 85. She/He plans on taking a sample to test her belief.
The correct set of hypotheses is
a. H0:  < 85 Ha:  85
b. H0:  85 Ha:  > 85
c. H0:  85 Ha:  < 85
d. H0:  > 85 Ha:  85
10.The manager of an automobile dealership is considering a new bonus plan
in order to increase sales. Currently, the mean sales rate per salesperson is
five automobiles per month. The correct set of hypotheses for testing the
effect of the bonus plan is
a. H0:  < 5 Ha:  5
b. H0:  5 Ha:  > 5
c. H0:  > 5 Ha:  5
d. H0:  5 Ha:  < 5
11.A null hypothesis is that the mean height of men and women are the same.
The alternative hypothesis is that men have a longer mean height than
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women. Which of the following is the correct way to state the null
hypothesis?
a. H0: p
b. H 0 : x1  x2  0
c. H0: p1 – p2 = 0
d. H0:  = 0
12.Refer to Q11. A statistical test is performed for assessing if men have a
longer mean height than women. The p-value is 0.225. Which of the
following is the most appropriate way to state the conclusion?
a. The mean height of the populations of men and women are identical.
b. There is not enough evidence to say that that the populations of men
and women have different mean height.
c. Men have a greater mean height than women.
d. The probability is 0.225 that men and women have the same mean
height.
13.Sample sizes n1 = 100, n2 = 100 and numbers x1 = 39, x2 = 41 of successes to
find the pooled estimate 𝑝̅ .
a. 0.360
b. 0.400
c. 0.800
d. 0.450
14.If the regression equation is 𝑌̂ = 2 – 0.4X, what is the value of 𝑌̂when X = –
3?
a. 0.8
b. 3.2
c. -10.0
d. 14
15.Which of the following can not be answered from a regression equation?
a. Predict the value of y at a particular value of x.
b. Estimate the slope between y and x.
c. Estimate whether the linear association is positive or negative.
d. Estimate whether the association is linear or non-linear
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16. The equation of a regression line is called the regression equation.
a. True
b. False
17. The regression line for a set of points is given by 𝑌̂ = 12 6x.
What is the slope of the line?
a. -12
b. -6
c. +6
d. 12
18. If the correlation coefficient between X and Y is one, then there is no linear
Correlation.
a. True
b. False
19. Two samples are independent if the sample values from one population are
not related to or somehow naturally paired or matched with the sample values
from the other population.
a. True
b. False
20. A two-tailed test is one where:
a. results in only one direction can lead to rejection of the null hypothesis
b. negative sample means lead to rejection of the null hypothesis
c. results in either of two directions can lead to rejection of the null
hypothesis
d. no results lead to the rejection of the null hypothesis
21. The chi-square goodness-of-fit test can be used to test for:
a. significance of sample statistics
b. difference between population means
c. normality
d. probability
22. The ANOVA test is based on which assumptions?
I.
the sample are randomly selected
II.
the population variances are all equal to some common variance
III.
the populations are normally distributed
IV. the populations are statistically significant
a.
b.
c.
d.
All of the above
II and III only
I, II, and III only
I, and III only
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23. The chi-square test can be too sensitive if the sample is:
a. very small
b. very large
c. homogeneous
d. predictable
24. One-way ANOVA is used when:
a. analyzing the difference between more than two population means
b. analyzing the results of a two-tailed test
c. analyzing the results from a large sample
d. analyzing the difference between two population means
25. Typically one-way ANOVA is used in which of the following situations?
I.
there are several distinct populations
II.
there are two sample populations over 4000
III.
randomized experiments
IV. randomly selected populations
a. All of the above
b. II and III only
c. I, II, and III only
d. I, and III only
26. The chi-square test is not very effective if the sample is:
a. small
b. large
c. irregular
d. heterogeneous
27. In a one-way analysis of variance, the “Sum of Squared Errors” is a
measure of the
a. variation among population means
b. variation among individuals within groups
c. variation among observed sample means
d. variation among sample sizes
28. When a one-way analysis of variance test is done, what probability
distribution is used to find the p-value?
a. F-distribution
b. normal distribution
c. Chi-square distribution
d. t-distribution
29. If 1, 2 and 3 are the population means of GPA for the about right,
overweight and underweight groups, respectively, then the alternative
hypotheses tested by ANOVA:
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a. 1, 2 and 3 are all different.
b. At least two of 1, 2 and 3 are different from each other.
c. 1 = 2  3
d. 1 > 2 > 3
30. A one-way analysis of variance will be done to compare systolic blood
pressures in three different age groups. What is the correct statement of the
null hypothesis?
a. 1  2  3
b. 1  2  3
c. ̅̅̅
𝑥1 = ̅̅̅
𝑥2 = ̅̅̅
𝑥3
d. ̅̅̅
𝑥1  ̅̅̅
𝑥2  ̅̅̅
𝑥3
Q. 1 2
3 4
5
6 7
8 9
10 11 12 13 14 15
A.
Q. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
A.
Section –II
Answer the following Short Type Questions
(12 marks, 2 Mark Each)
1. Assume that a simple random sample has been selected from a
normally distributed population. Test the claim that the mean age of
the prison population in one city is less than 26 years. Sample data
are summarized as n = 25, 𝑋̅ = 24.4 years, and s = 9.2 years. Use a
significance level of  = 0.05, p-value = 0.1966, critical value : t = 1.711
2. For the Salary _ Experience data set, test to see if there is a difference in
salaries for employees who selection into their current position was from within
the company (internal employees) versus who were selected into their position
from outside the company (external employees).
The XL output is as follows. Comparing Salaries (x$1000)
t-test : two-sample Assuming non-equal variances
Continuous…………..
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mean
variance
observations
Pooled variance
Hypothesized Mean Difference
df
T stat
P(T<= t) one- tail
t-critical one -tail
P(T<= t) two- tail
t-critical one -tail
External salary A
Internal salary B
78.35
87.94
62
83.08
0
148
7.581
0.000
1.655
0.000
1.975
66.90
79.68
88
a. State the null hypotheses and alternative hypotheses.
b. What is test statistics give answer with formula.
c. Conclusion?
3. A carpet company advertises that it will deliver your carpet within 15 days
of purchase. A sample of 49 past customers is taken. The average delivery
time in the sample was 16.2 days. The standard deviation of the
population () is known to be 5.6 days.
a. Using the critical value approach, test to determine if their advertisement
is legitimate. Let  = .05.
b. Using the p-value approach, test the hypotheses at the 5% level of
significance.
4. A company wants to study the relationship between an employee's length of
employment and their number of workdays absent. The company collected
the following information on a random sample of seven employees.
Number of Workdays Absent
Length of Employment (in yrs)
2
5
3
6
3
9
5
4
7
2
7
2
8
0
Q1. What is the slope of the linear equation?
Q2. What is the Y intercept of the linear equation?
5. Students at multiple grade schools were asked what their personal
goal ( grades, be good and bad at sports) was and what good grades
and bad grades were. The data is in table ("Popular kids data file,"
2013). Calculate the Chi-square test.
Page 8 of 11
Table: Personal Goal and Importance of Grades
Goal
Grades Importance Rating
Good
Bad
Grades
70
66
Sports
10
24
Column Total
80
90
Row Total
136
34
170
6. While conducting a one-way ANOVA comparing five treatments with 10
observations per treatment, you compute SST = 250 and MSE = 3.
Construct ANOVA table and find the value of F?
Section –III
Answer the following Long Type Questions
(18 marks, 3 Mark Each)
1. Tata- Corporation is a company has a stable workforce with little turnover.
They have been in business for 50 years. It has more than 10,000
employees.
The company has always promoted the idea that its employees stay with
them for a very long time, and it has used the following line in
its recruitment brochures: "The average tenure of our employees is 20
years."
Since Tata-corporation isn't quite sure if that statement is still true, a
random sample of 100 employees is taken and the average age turns out to
be 19 years with a standard deviation of 4 years. Can Tata continue to make
its claim, or does it need to make a change?
a. State the hypotheses.
b. What is the test statistic? (Note that the sample is randomly selected
from a population that is assumed to be normally distributed and/or we
have a large sample)
c. Specify the significance level
d. Calculations: The calculated z value is -2.5
It has p = 0.0062
Reject or fail to reject the null?
e. Conclusion?
f. What type of the error?
Page 9 of 11
2. An airport official wants to assess if the flights from one airline (Airline 1)
are less delayed than flights from another airline (Airline 2). Let 1 = average
delay for Airline 1 and  2 = average delay for Airline 2. A random sample of
10 flights for Airline 1 shows an average of 9.5 minutes delay with a
standard deviation of 3 minutes. A random sample of 10 flights for Airline 2
shows an average of 12.63 minutes delay with a standard deviation of 3
minutes. Assume delay times are normally distributed, but do not assume
the population variances are equal. Use the conservative “by hand”
estimate for the degrees of freedom. p-value = 0.022
a. What are the appropriate null and alternative hypotheses?
b. What is the value of the test statistic?
c. For a significance level of  = 0.05, are the results statistically
significant?
d. Which of the following is an appropriate conclusion?
3. Assume you send your salespeople to a “customer service” training
workshop. Has the training made a difference in the number of
complaints? What is hypotheses? Calculate test statistics and give
conclusion. You collect the following data. (Test at the 0.01 level).
4. Find Linear correlation coefficient between X and Y for the following data:
Hours X
Score Y
1
1
1
3
3
2
4
5
6
4
7
5
8
7
8
8
5. Suppose a die throw, check it is fair or not. If it is fair then the
proportion for each value should be the same. It is need to find the
observed frequencies and to accomplish this roll the die 500 times
and count how often each side comes up. The data is in table. Do the
data show that the die is fair? Test at the 5% level. 2 cdf 5≈0.913
Page 10 of 11
Table: Observed Frequencies of Die
Die values
1
2
3
Observed Frequency 78
87
87
4
76
5
85
6
87
Total
100
1. State the null and alternative hypotheses and the level of significance
2. Find the 2 -test.
3. Conclusion?
6. While conducting a one-way ANOVA comparing three salary/experience
group
Use the Salary/Experience data set. At the 0.05 significance level, is there a
difference in mean salary among the experience groups of the employees?
High Level Experience:
employees with 10 or more years of
experience in the field
Moderate Experience:
employees with 6 to 9 years of
experience in the field
Low Experience:
employees with 5 or less years of
experience in the field
with following observation in table,
give appropriate hypotheses. Construct ANOVA table and find the value
of F and conclusion? Fcrt = 3.0576 , p-value = 0.00005
salary by experience
summary
Group
H EXP Sal
H EXP Sal
H EXP Sal
count
48
57
45
sum
3255
4059
3431
Good luck
Page 11 of 11
average
67.8
71.2
76.2
variance
84.9
111.7
117.2