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IITM BS Week 10 Statistics 2 Questions | Prasnya
Statistics 2 > Week 10
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44Q
01
Let
X
1
,
…
,
X
100
X_1, \dots, X_{100}
X
1
,
…
,
X
100
be a sample from a normal distribution having a variance of 25. We wish to test the hypothesis
H
0
:
μ
=
0
H_0: \mu = 0
H
0
:
μ
=
0
against
H
1
:
μ
=
1.5
H_1: \mu = 1.5
H
1
:
μ
=
1.5
. Consider a test that rejects
H
0
H_0
H
0
for
X
ˉ
>
c
\bar{X} > c
X
ˉ
>
c
, where
X
ˉ
\bar{X}
X
ˉ
is the sample mean. Find the value of
c
c
c
at a significance level
α
=
0.05
\alpha = 0.05
α
=
0.05
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
10 May 2026
02
Enter the correct option number for
A
\mathbf{A}
A
.
Comprehension
EASY
0.5 marks
10 May 2026
03
Enter the correct option number for
B
\mathbf{B}
B
.
Comprehension
EASY
0.5 marks
10 May 2026
04
Enter the correct option number for
C
\mathbf{C}
C
.
Comprehension
EASY
0.5 marks
10 May 2026
05
Enter the correct option number for
D
\mathbf{D}
D
.
Comprehension
MEDIUM
0.5 marks
10 May 2026
06
Calculate the value for
E
\mathbf{E}
E
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
1 marks
10 May 2026
07
Define the null hypothesis and the alternative hypothesis.
Comprehension
EASY
2 marks
10 May 2026
08
Find the significance level of the test. Enter the answer correct to three decimal places.
Comprehension
HARD
3 marks
10 May 2026
09
Define the null hypothesis and the alternative hypothesis.
Comprehension
EASY
2 marks
10 May 2026
10
Find the significance level of the test. Enter the answer correct to three decimal places.
Comprehension
HARD
3 marks
10 May 2026
11
Suppose
X
∼
N
(
μ
,
σ
2
)
X \sim N(\mu, \sigma^2)
X
∼
N
(
μ
,
σ
2
)
with an unknown
σ
\sigma
σ
. For
n
=
16
n = 16
n
=
16
i.i.d. samples of
X
X
X
, the observed sample mean is
10.2
10.2
10.2
and the sample standard deviation is
3
3
3
. Let the null and alternative hypothesis be
H
0
:
μ
=
9.5
H_0: \mu = 9.5
H
0
:
μ
=
9.5
and
H
A
:
μ
>
9.5
H_A: \mu > 9.5
H
A
:
μ
>
9.5
. Suppose
T
=
X
ˉ
−
9.5
3
/
16
T = \frac{\bar{X} - 9.5}{3/\sqrt{16}}
T
=
3/
16
X
ˉ
−
9.5
. Consider a test that rejects
H
0
H_0
H
0
if
T
>
c
T > c
T
>
c
for some constant
c
c
c
. What is the level of significance in terms of 'c'?
Single correct
MEDIUM
3 marks
13 April 2025
12
A hospital claims that the average waiting time in the emergency room is 20 minutes with a standard deviation of 6 minutes. A sample of 36 patients has a mean waiting time of 22 minutes. Let the null and alternative hypotheses be
H
0
:
μ
=
20
H_0: \mu = 20
H
0
:
μ
=
20
and
H
A
:
μ
>
20
H_A: \mu > 20
H
A
:
μ
>
20
. Consider a test that rejects
H
0
H_0
H
0
if
X
ˉ
>
c
\bar{X} > c
X
ˉ
>
c
for some constant
c
c
c
. What is the value of 'c' at 5% level of significance? Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
13 April 2025
13
Find the P-value. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
13 April 2025
14
Find the power of the test against the alternative
μ
=
5.5
\mu = 5.5
μ
=
5.5
. Enter the answer correct to two decimal places.
Comprehension
HARD
2 marks
13 April 2025
15
Which of the following statement(s) is(are) correct?
Multiple correct
MEDIUM
3 marks
22 December 2024
16
State the null and alternative hypotheses.
Comprehension
EASY
2 marks
22 December 2024
17
What conclusion will you make for the given test?
Comprehension
MEDIUM
3 marks
22 December 2024
18
Consider
36
36
36
samples
X
1
,
X
2
,
…
,
X
36
∼
iid Normal
(
μ
,
36
)
X_1, X_2, \ldots, X_{36} \sim \text{iid Normal}(\mu, 36)
X
1
,
X
2
,
…
,
X
36
∼
iid Normal
(
μ
,
36
)
. Let the null and alternate hypothesis be
H
0
:
μ
=
150
H_0: \mu = 150
H
0
:
μ
=
150
and
H
A
:
μ
≠
150
H_A: \mu \neq 150
H
A
:
μ
=
150
. Suppose
T
=
X
1
+
X
2
+
…
+
X
36
36
T = \frac{X_1 + X_2 + \ldots + X_{36}}{36}
T
=
36
X
1
+
X
2
+
…
+
X
36
. Consider a test that rejects
H
0
H_0
H
0
if
∣
T
−
150
∣
>
c
|T - 150| > c
∣
T
−
150∣
>
c
for some constant
c
c
c
. What should be the critical value for the test at a significance level of
0.05
0.05
0.05
?
Single correct
MEDIUM
3 marks
01 September 2024
19
What should be the null hypothesis and alternative hypothesis?
Comprehension
EASY
1 marks
01 September 2024
20
Find the critical value c at a significance level of 0.05. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
01 September 2024
21
What conclusion should be made from the test hypotheses?
Comprehension
EASY
1 marks
01 September 2024
22
Consider 100 samples
X
1
,
X
2
,
…
,
X
100
∼
i.i.d. Normal
(
μ
,
36
)
X_1, X_2, \dots, X_{100} \sim \text{i.i.d. Normal}(\mu, 36)
X
1
,
X
2
,
…
,
X
100
∼
i.i.d. Normal
(
μ
,
36
)
. Let the null and alternative hypothesis be
H
0
:
μ
=
4
H_0: \mu = 4
H
0
:
μ
=
4
and
H
A
:
μ
=
−
4
H_A: \mu = -4
H
A
:
μ
=
−
4
. Suppose
T
=
X
1
+
X
2
+
⋯
+
X
100
100
T = \frac{X_1 + X_2 + \dots + X_{100}}{100}
T
=
100
X
1
+
X
2
+
⋯
+
X
100
. Consider a test that rejects
H
0
H_0
H
0
if
T
<
c
T < c
T
<
c
for some constant
c
c
c
. What is the level of significance in terms of '
c
c
c
'?
Single correct
MEDIUM
3 marks
28 April 2024
23
Consider the following situation and match it with suitable test statistic and hypothesis test: Suppose we observe samples from a normal distribution, where the variance is unknown. We want to check whether the mean is greater than
μ
\mu
μ
. What test statistic and test can be applied for this situation?
Single correct
EASY
3 marks
28 April 2024
24
What null hypothesis and alternative hypothesis should the analyst consider?
Comprehension
EASY
2 marks
28 April 2024
25
Which of the following conclusions will the analyst reach at the specified significance levels?
Comprehension
MEDIUM
3 marks
28 April 2024
26
Consider 100 samples
X
1
,
X
2
,
…
,
X
100
∼
iid Normal
(
μ
,
25
)
X_1, X_2, \dots, X_{100} \sim \text{iid Normal}(\mu, 25)
X
1
,
X
2
,
…
,
X
100
∼
iid Normal
(
μ
,
25
)
. Let the null and alternative hypothesis be
H
0
:
μ
=
−
2
H_0: \mu = -2
H
0
:
μ
=
−
2
and
H
A
:
μ
=
2
H_A: \mu = 2
H
A
:
μ
=
2
. Suppose
T
=
X
1
+
X
2
+
⋯
+
X
100
100
T = \frac{X_1 + X_2 + \dots + X_{100}}{100}
T
=
100
X
1
+
X
2
+
⋯
+
X
100
. Consider a test that rejects
H
0
H_0
H
0
if
T
>
c
T > c
T
>
c
for some constant
c
c
c
. What is the significance level of the test in terms of '
c
c
c
'?
Single correct
HARD
3 marks
24 December 2023
27
Define null hypothesis and alternative hypothesis.
Comprehension
EASY
2 marks
24 December 2023
28
Find the power of the test for
μ
=
11
\mu = 11
μ
=
11
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
24 December 2023
29
Consider the following situation and match it with suitable test statistic and hypothesis test: Suppose we observe samples from a normal distribution, where the variance is unknown. We want to check whether the mean is greater than
μ
\mu
μ
. What test statistic and test can be applied for this situation?
Single correct
EASY
3 marks
03 September 2023
30
Which of the following statement(s) is (are) correct?
Multiple correct
MEDIUM
3 marks
03 September 2023
31
Define null hypothesis and alternative hypothesis.
Comprehension
EASY
2 marks
03 September 2023
32
Choose the set of correct options.
Comprehension
MEDIUM
3 marks
03 September 2023
33
Which of the following statement(s) is/are correct?
Multiple correct
MEDIUM
3 marks
30 April 2023
34
Define null hypothesis and alternative hypothesis.
Comprehension
EASY
2 marks
30 April 2023
35
Find the significance level of the test. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
30 April 2023
36
Which of the following statements are correct?
Multiple correct
MEDIUM
3 marks
11 December 2022
37
Consider 100 samples
X
1
,
X
2
,
…
,
X
100
∼
iid Normal
(
μ
,
16
)
X_1, X_2, \dots, X_{100} \sim \text{iid Normal}(\mu, 16)
X
1
,
X
2
,
…
,
X
100
∼
iid Normal
(
μ
,
16
)
. Let the null and alternative hypothesis be
H
0
:
μ
=
1
H_0 : \mu = 1
H
0
:
μ
=
1
and
H
A
:
μ
=
−
1
H_A : \mu = -1
H
A
:
μ
=
−
1
. Suppose
T
=
X
1
+
X
2
+
⋯
+
X
100
100
T = \frac{X_1 + X_2 + \dots + X_{100}}{100}
T
=
100
X
1
+
X
2
+
⋯
+
X
100
. Consider a test that rejects
H
0
H_0
H
0
if
T
>
c
T > c
T
>
c
for some constant
c
c
c
. What should be the critical value for the test at a significance level of 0.05?
Single correct
HARD
3 marks
11 December 2022
38
Consider the following situations and match them with suitable test statistics and hypothesis tests: Suppose we observe samples from a normal distribution, where the variance is known. We want to check whether the mean is greater than
μ
\mu
μ
. What test statistic and test can be applied for this situation?
Single correct
EASY
3 marks
11 December 2022
39
Define null hypothesis and alternative hypothesis.
Comprehension
EASY
2 marks
11 December 2022
40
Find the significance level of the test. Enter the answer correct to three decimal places.
Comprehension
HARD
3 marks
11 December 2022
41
Consider the null and alternative hypothesis
H
0
:
μ
=
0
,
H
A
:
μ
>
0
H_0: \mu = 0, H_A: \mu > 0
H
0
:
μ
=
0
,
H
A
:
μ
>
0
. In which of the following cases can we reject the null hypothesis?
Multiple correct
EASY
2 marks
07 August 2022
42
Define null hypothesis and alternative hypothesis.
Comprehension
EASY
1 marks
07 August 2022
43
Find the P-value. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
07 August 2022
44
Choose the set of correct options.
Comprehension
MEDIUM
3 marks
07 August 2022
Showing 44 questions.
Complete question index for this section:
Question 1 (integer):
Question 2 (comprehension):
Question 3 (comprehension):
Question 4 (comprehension):
Question 5 (comprehension):
Question 6 (comprehension):
Question 7 (comprehension):
Question 8 (comprehension):
Question 9 (comprehension):
Question 10 (comprehension):
Question 11 (single):
Question 12 (integer):
Question 13 (comprehension):
Question 14 (comprehension):
Question 15 (multiple):
Question 16 (comprehension):
Question 17 (comprehension):
Question 18 (single):
Question 19 (comprehension):
Question 20 (comprehension):
Question 21 (comprehension):
Question 22 (single):
Question 23 (single):
Question 24 (comprehension):
Question 25 (comprehension):
Question 26 (single):
Question 27 (comprehension):
Question 28 (comprehension):
Question 29 (single):
Question 30 (multiple):
Question 31 (comprehension):
Question 32 (comprehension):
Question 33 (multiple):
Question 34 (comprehension):
Question 35 (comprehension):
Question 36 (multiple):
Question 37 (single):
Question 38 (single):
Question 39 (comprehension):
Question 40 (comprehension):
Question 41 (multiple):
Question 42 (comprehension):
Question 43 (comprehension):
Question 44 (comprehension):
