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qnt/275 statistics for decision making, university of phoenix

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Practice Set 4

QNT/275 Version 6

University of Phoenix Material

Practice Set 4

Practice Set 4

1. Find z for each of the following confidence levels. Round to two decimal places.

A. 90%

NormInv(

1−0.90

) = ±1.645

2

B. 95%

NormInv(

1−0.95

) = ±1.960

2

C. 96%

NormInv(

1−0.96

) = ±2.054

2

D. 97%

NormInv(

1−0.97

) = ±2.170

2

E. 98%

NormInv(

1−0.98

) = ±2.326

2

F. 99%

NormInv(

1−0.99

2

) = ±2.576

2. For a data set obtained from a random sample, n = 81 and x = 48.25. It is known

that σ = 4.8.

A. What is the point estimate of μ? Round to two decimal places

The point estimate μ is equal to 48.25

B. Make a 95% confidence interval for μ. What is the lower limit? Round to two decimal

places.

Copyright © 2017 by University of Phoenix. All rights reserved.

1

Practice Set 4

QNT/275 Version 6

x̅ − Zα/2

σ

√n

48.25 − 1.96 ∗

4.8

√81

48.25 − 1.05

𝐋𝐨𝐰𝐞𝐫 𝐥𝐢𝐦𝐢𝐭 = 𝟒𝟕. 𝟐𝟎

C. Make a 95% confidence interval for μ. What is the upper limit? Round to two decimal

places.

x̅ + Zα/2

σ

√n

48.25 + 1.96 ∗

4.8

√81

48.25 + 1.05

𝐔𝐩𝐩𝐞𝐫 𝐥𝐢𝐦𝐢𝐭 = 𝟒𝟗. 𝟑𝟎

D. What is the margin of error of estimate for part b? Round to two decimal places.

E = Zα/2

σ

√n

4.8

E = 1.96 ∗

√81

𝐄 = 𝟏. 𝟎𝟓

3. Determine the sample size (nfor the estimate of μ for the following.

A. E = 2.3, σ = 15.40, confidence level = 99%. Round to the nearest whole number.

α = 1 – 0.99 = 0.01

σ

n = (zα⁄2 ( ))2

E

15.40 2

n = (z0.01⁄2 (

))

2.3

15.40 2

n = (2.576 (

))

2.3

𝐧 = 𝟐𝟗𝟕

B. E = 4.1, σ = 23.45, confidence level = 95%. Round to the nearest whole number.

Copyright © 2017 by University of Phoenix. All rights reserved.

2

Practice Set 4

QNT/275 Version 6

α = 1 – 0.95 = 0.05

σ

n = (zα⁄2 ( ))2

E

15.40 2

n = (z0.05⁄2 (

))

2.3

23.45 2

n = (1.960 (

))

4.1

𝐧 = 𝟏𝟐𝟔

C. E = 25.9, σ = 122.25, confidence level = 90%. Round to the nearest whole number.

α = 1 – 0.90 = 0.10

σ

n = (zα⁄2 ( ))2

E

15.40 2

n = (z0.10⁄2 (

))

2.3

122.25 2

n = (1.645 (

))

25.9

𝐧 = 𝟔𝟎

4. True or False.

a. The null hypothesis is a claim about a population parameter that is assumed to be false

until it is declared false.

A. True

B. False

b. An alternative hypothesis is a claim about a population parameter that will be true if the

null hypothesis is false.

A. True

B. False

c. The critical point(s) divide(s) is some of the area under a distribution curve into rejection

and nonrejection regions.

A. True

B. False

d. The significance level, denoted by α, is the probability of making a Type II error, that is,

the probability of rejecting the null hypothesis when it is actually true.

A. True

B. False

e. The nonrejection region is the area to the right or left of the critical point where the null

hypothesis is not rejected.

A. True

Copyright © 2017 by University of Phoenix. All rights reserved.

3

Practice Set 4

QNT/275 Version 6

B. False

5. Fill in the blank. The level of significance in a test of hypothesis is the probability of making a

_Type I error_. It is the area under the probability distribution curve where we reject H0.

A. Type I error

B. Type II error

C. Type III error

6. Consider H0: μ = 45 versus H1: μ < 45. A random sample of 25 observations produced a sample

mean of 41.8. Using α = .025 and the population is known to be normally distributed with σ = 6.

A. What is the value of z? Round to two decimal places.

x−μ

σ

( )

√n

41.8 − 45

Z=

6

(

)

√25

𝐙 = −𝟐. 𝟔𝟕

Z=

B. Would you reject the null hypothesis?

For α = .025 the critical value is -1.96. This value is greater than -2.67, then reject the

null hypothesis.

1. Reject Ho

2. Do not reject Ho

7. The following information is obtained from two independent samples selected from two

normally distributed populations.

n1 = 18

x1 = 7.82

σ1 = 2.35

n2 =15

x2 =5.99

σ2 =3.17

A. What is the point estimate of μ1 − μ2? Round to two decimal places.

μ1 − μ2 = 7.82 – 5.99 = 1.83

B. Construct a 99% confidence interval for μ1 − μ2. Find the margin of error for this

estimate.

Round to two decimal places.

Copyright © 2017 by University of Phoenix. All righ...

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