# statistic questions

User Generated

fnenu711

Mathematics

## Description

Hello, there are 6 statistics problems in attachment.

A,B,C,D,E,F

The book is also available in the attached file.

Thank you

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here is solution enclosed ;kindly ask if any query.regards

Question 1
(a)

Normal Distribution
N(µ,σ)
0.12
0.1
0.08
f(x) 0.06
0.04
0.02
0
0

5

10

15

20

25

x

Table(x,y) is enclosed in excel file
(b)
17

F ( x  17) 



1
2 2

e

 ( x )2

 2 2

dx 

1
2 2

17

e

 ( x  20) 2 / 32

dx  0.1587



(c)
 X   12  20 
P X  12   P

  PZ  2  0.0228
4 
 

(d)

Z
(e)

X 

22  20
 0.5
4

30

35

40

Z 0.1  11.28
x

 1.28

x    1.28  20  1.28  4  25.12
90th percentile is x  25.12

Question B
(a) Standard deviation of the mean 

N

5
25

1

(b)
 25  40 X   34  40 

P 25  X  34   P

5

5
1

 P 3  Z  1.2 
 PZ  1.2   PZ  3

 1  PZ  1.2   1  PZ  3
 1  0.8849  1  0.9987
 0.1138

Thus, there is 0.1138 probability that X is between 25 and 34.
(c)
There is 0.997 probability that an individual data point X is between 25 and 34.

Question C
The provided sample mean is x  7.4 and the sample standard deviation is s=2.6, and
the sample size is n = 15.

(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: μ ≥ 9
Ha: μ < 9

This corresponds to a left-tailed test, for which a t-test for one mean, with
unknown population standard deviation will be used.
(2) Rejection Region
Based on the information provided, the significance level is α=0.05, and the
critical value for a left-tailed test is t c  1.761 .
The rejection region for this left-tailed test is R = {t: t < -1.761}
(3) Test Statistics
The t-statistic is computed as follows:
t

x

7. 4  9
 2.383
2.6

n

15

(4) Decision about the null hypothesis
Since it is observed that t =−2.383 0.50

This corresponds to a right-tailed test, for which a z-test for one population proportion
needs to be used.
(2) Rejection Region
Based on the information provided, the significance level is α=0.01, and the critical
value for a right-tailed test is zc=2.33.
The rejection region for this right-tailed test is R = {z: z > 2.33}
(3) Test Statistics
The z-statistic is computed as follows:
p

p  p0
p o (1  p 0 )
N

0.3874  0.5
0.5  0.5
111

 2.373

(4) Decision about the null hypothesis
Since it is observed that z =−2.373≤zc=2.33, it is then concluded that the null
hypothesis is not rejected.
Using the P-value approach: The p...

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Anonymous
Really great stuff, couldn't ask for more.

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