Homework answers / question archive / 1)What is the sampling distribution of when sample of size 50 is used?       Is normal due to the Central Limit Theorem Is normal due to the Chebyshev's Theorem Is not normal because the sample size is too small Is not normal because the sample size is too large   2

1)What is the sampling distribution of when sample of size 50 is used?       Is normal due to the Central Limit Theorem Is normal due to the Chebyshev's Theorem Is not normal because the sample size is too small Is not normal because the sample size is too large   2

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1)What is the sampling distribution of when sample of size 50 is used?

 

 

 

Is normal due to the Central Limit Theorem

Is normal due to the Chebyshev's Theorem

Is not normal because the sample size is too small

Is not normal because the sample size is too large

 

2. Suppose that we reduce the sample size from 50 to 25. The sampling distribution ofwill be normal only if

X has a bi-modal distribution

X has a normal distribution

X has a uniform distribution

X has a skewed distribution

 

3. What is the probability in percentage that a random sample of 50 gas stations will provide an average gas price (Xbar) that is more than $6.00?

3.52%

2.18%

2.96%

4.12%

 

4. What is the probability that a random sample of 50 gas stations will provide an average gas price (Xbar) that is within $0.50 of the population mean (mu)? ( + - from population mean)

21%

17%

65%

5%

 

The following 4 questions are based on this information: Census indicates that the proportion of adult women in the United States is 55% (p = 0.55).We will take a random sample of 500 U.S. adults.

5. The sampling distribution of , the sample proportion of U.S. adult who are women, is:

 

is normal because np >= 5 and n(1-p)>=5

is not normal because the sample size is too small

is normal because the only requirement is for n to be greater than 30 and that is met

is not normal because n > 600

 

6. The standard error (SE) of pbar is:

0.018

0.034

0.041

0.022

 

7. What is the probability that a random sample of 500 US Adults will provide a sample proportion (pbar) that is within 0.07 of the population proportion (p)?

99%

1%

89%

5%

 

8. Say, you took a random sample of 500 US Adults, and found out that the sample proportion (pbar) for this sample to be 0.31

This is a rare finding because the likelihood of pbar = 0.31 is quite small as we saw in the previous question

This is NOT a rare finding because the likelihood of pbar = 0.31 is quite large as we saw in the previous question.

 

 

9. The Standard Error (SE) of Xbar is:

 

0.006

0.002

0.03

1.02

 

10. The Critical Value (CV) used for a 95% Interval Estimate is:

 

0.025

1.64

1.96

0.05

 

11. The 95% Confidence Interval Estimate of µ is:

 

1.02 ± 0.059

1.02 ± 0.012

1.02 ± 0.034

1.02 ± 0.213

 

12. Suppose you think that average weight of a cereal box of Granola Crunch is 0.9 pounds. Inlight of the sample evidence and at the 5% level of significance,

Your claim is not statistically justified.

Your claim is statistically justified.

 

13 .If we increase the confidence level (1-α) from 0.95 to 0.99, the margin of error (ME) of the confidence interval estimate will

stays the same

decrease

zero

increase

 

U.S. workers is normally distributed.

14. The Standard Error (SE) of Xbar is:

 

2.87

2.39

3.16

3.84

 

15. The Critical Value (CV) needed for 90% Confidence Interval Estimation is

1.96

1.25

2.16

1.68

 

16. The 90% Confidence Interval Estimate of µ is:

 

20 ± 4.007

20 ± 2.085

20 ± 3.684

20 ± 1.154

 

17. Suppose CEO of a company claims that the yearly average vacation days of all U.S.workers is 18 days. In light of the sample evidence and at the 10% level of significance,

 

We can reject the CEO's claim.

We cannot reject the CEO's claim. (Within the range 20+)

 

18. For the confidence level (1 - α) = 0.99, the critical value (CV) is:

 

2.57

1.96

1.64

3.12

 

19. How large a sample (rounded up) would be needed to estimate this year's mean with a 99% confidence and a margin of error of 4 seconds? Use last year's standard deviation as the population standard deviation (σ).

 

17

11

27

32

 

20. For the confidence level (1 - α) = 0.95, the critical value (CV)

 

1.96

1.64

2.57

2.12

 

21. How large a sample (rounded up) would be needed to estimate this year's mean with a 95% confidence and a margin of error of 2 seconds? Use last year's standard deviation as the population standard deviation (σ).

 

51

62

47

29

22. The Standard Error (SE) of pbar is:

 

0.044

0.016

0.266

0.384

 

23. The Critical Value (CV) needed for 90% confidence interval estimation is:

 

1.64

1.96

1.28

2.34

 

24. The 90% confidence interval estimate of p is:

 

0.44 ± 0.03

0.44 ± 0.15

0.44 ± 0.12

0.44 ± 0.005

 

25. Currently the sample size (n) is 1000. If we were to decease n to 500, the margin of error(ME) of the confidence interval estimate would

 

zero

decrease

increase

constant

26. State the null and alternative hypotheses:

 

H(0): µ <= 150 & H(a): µ > 150

H(0): µ >= 150 & H(a): µ < 150

 

27. The Standard Error (SE) of Xbar is:

 

2.15

2.49

5.42

3.26

 

28. The Test Statistics value is:

 

4.20

2.22

-2.56

-4.19

 

29. The P-Value is:

 

0.05

0.0000004

0.000013

0.0038

 

30. at alpha = 0.05, and using the P-value:

 

We do not reject H(0)

We reject H(0) in favor of H(a)

 

 

31. What is the Point Estimate of the difference between the population mean remodeling costs for the two types of projects?

1.28

1.03

-1.92

-1.60

 

32. What is the Margin of Error if alpha = 0.1

2.70

3.11

1.29

4.66

 

33. The 90% Confidence Interval Estimate for the difference between the two population means:

-1.60 ± 2.70

-1.92 ± 1.29

1.28 ± 3.11

1.03 ± 2.70

 

 

34. Develop the Hypotheses:

 

H(0): µd >= 0 & H(a): µd < 0

H(0): µd <= 0 & H(a): µd > 0

 

35. What is the average of the difference?

 

1.77

2.43

3.51

0.63

 

36. What is the value of the sample standard deviation of the difference?

 

2.66

1.30

1.96

3.17

 

37. At alpha = 0.05, What is the P-Value?

 

0.11

0.03

0.08

0.16

 

38. With respect to the P-value from the previous question, We:

 

Do no reject H(0) because P-value > alpha

Reject H(0) because P-value is < alpha