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home / study / math / statistics and probability / statistics and probability questions and answers / 23. construct a 95% confidence interval for data sets a and b. data sets a and b are dependent. ...

Question: 23. Construct a 95% confidence interval for data sets A and B. Data sets A and B are dependent. ...

23. Construct a 95% confidence interval for data sets A and B. Data sets A and B are dependent. Round to the nearest tenth.

A |
:30 |
28 |
47 |
43 |
31 |
||

B |
:28 |
24 |
25 |
35 |
22 |

A.

( − 0.7,18.7)

B.

( − 1.3,9.0)

C.

( − 0.1,12.8)

D.

( − 15.3,15.4)

22. Construct a 95% confidence interval for μ1−μ2. Two samples are randomly selected from normal populations. The sample statistics are given below.

Assume that σ2/1=σ2/2.

n1= 11, n2= 18, x1= 4.8, x2= 5.2, s1= 0.76,s2=0.51

A.

( − 4.152,3.981)

B.

( − 0.883,0.083)

C.

( − 1.762,1.762)

D.

( − 2.762,2.762)

21. Compute the standardized test statistic, X2 , to test the claim σ2=30.1 if n= 12, s2=25.2, and α=0.05.

A.

0.492

B.

12.961

C.

9.209

D.

18.490

20. Find the critical value and rejection region for the type of t-test with level of significance (α and sample size n).

Two-tailed test, α=0.1, n=23

A.t0= −1.717 , t0=1.717 ; t<minus−1.717 , t>1.717

B.t0=−1.714, t0=1.714 ; t<−1.714 , t>1.714

C.t0= −1.321 , t0=1.321 ; t<−1.321, t>1.321

D.t0=1.717; t>1.717

19. Suppose you want to test the claim that μ1>μ2. Two samples are randomly selected from normal populations. The sample statistics are given below. Assume that σ2/1≠σ2/2. At a level of significance of α=0.01 , when should you reject H0 ?

n1= 18, n2= 13, x1=540 , x2=525 , s1= 40, s2=25

A.

Reject H0 if the standardized test statistic is greater than 1.699.

B.Reject H0 if the standardized test statistic is greater than 2.179.

C.Reject H0 if the standardized test statistic is greater than 3.055.

D.Reject H0 if the standardized test statistic is greater than 2.681.

18. Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed.

Claim: μ≠43 ; α= 0.05; σ=2.7

Sample statistics: x=42.1, n=35

A.

Fail to reject H0. There is not enough evidence at the 5% level of significance to support the claim.

B.

Reject H0. There is enough evidence at the 5% level of significance to support the claim.

C.

There is not enough information to decide.

17. Find the critical X2 -values to test the claim σ2=4.3 if n=12 and α=0.05.

A.

3.816, 21.920

B.

4.575, 19.675

C.

3.053, 24.725

D.

2.603, 26.757

Answer #1

23) Correct answer: Option (B)

95% Confidence interval:

-1.281788 < µ1-µ2 < 19.28179

22)Correct answer: Option (B)

95% Confidence interval:

-0.8825882 < µ1-µ2 < 0.0825882

21)Correct answer: Option (C)

20) Correct answer: Option (A.) t0= −1.717 , t0=1.717 ; t<minus−1.717 , t>1.717

18)

Test Statistic, z: (35-43) / (2.7/SQRT(35)) = -1.9720

Critical z: ±1.9600

P-Value: 0.0486

Here p-value < alpha 0.05 and Z value is not lies between Z critical values so reject H0

Correct answer: Reject H0. There is enough evidence at the 5% level of significance to support the claim.

17) Correct answer: (A)

Lower Critical ChiSq: 3.815745

Upper Critical ChiSq: 21.92007

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