## Description

Hello, there are 6 statistics problems in attachment.

A,B,C,D,E,F

PLEASE read each one of them carefully and solve.

The book is also available in the attached file.

Thank you

### Unformatted Attachment Preview

Purchase answer to see full attachment

## Explanation & Answer

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

PZ 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

PZ 1.2 PZ 3

1 PZ 1.2 1 PZ 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...