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Pg.431 1)The mean of the sampling...

Pg.431

1)The mean of the sampling distribution of means is equal to the mean of the population. T-F, and why or why not?

2) In the formula for the Confidence Interval for the Mean, if the Confidence Coefficient, z(α/2) = 1.65, what is the Confidence Level?

Pg. 432

1. Consider a population with µ =67.1 and σ=5.76 .

(A) Calculate the z-score for x̃ = 65.7 from a sample of size 40.

(B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text? Why or why not?

2.Given a level of confidence of 95% and a population standard deviation of 8, answer the following:

(A) What other information is necessary to find the sample size (n)?

(B) Find the Maximum Error of Estimate (E) if n = 59.

3. A sample of 136 golfers showed that their average score on a particular golf course was 82.77 with a standard deviation of 4.54.

Answer each of the following (show all work

and state the final answer to at least two decimal places.):

(A) Find the 99% confidence interval of the mean score for all 136 golfers.

(B) Find the 99% confidence interval of the mean score for all golfers if this is a sample of 90 golfers instead of a sample of 136.

(C) Which confidence interval is smaller and why?

4. Assume that the population of heights of female college students is approximately normally distributed with mean µ of 67.26 inches and standard deviation σ of 5.96 inches. A random sample of 78 heights is obtained. Show all work.

(A) Find the mean and standard error of the x̃ distribution

(B) Find P( x̃ > 67.50)

5. The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.82 inches and a standard deviation of 0.61 inches. Show all work.

(A) What percentage of the grapefruits in this orchard is larger than 5.78 inches?

(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample is greater than 5.78 inches?

6. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 99% confident that her estimate is correct. If the standard deviation is 4.11, how large a sample is needed to get the desired information to be accurate within 0.56 decibels?

Pg.432

1. Consider a normal population with µ = 25 and σ = 7.0.

(A) Calculate the standard score for a value x of 24.

(B) Calculate the standard score for a randomly selected sample of 45 with = 24.

(C) Explain why the standard scores of 24 are different between A and B above.

2. 2. Assume that the mean SAT score in Mathematics for 11th graders across the nation is 500, and that the standard deviation is 100 points. Find the probability that the mean SAT score for a randomly selected group of 150 11th graders is between 513 and 487.

3. Assume that a sample is drawn and z(α/2) = 1.96 and σ = 30. Answer the following questions:

(A)If the Maximum Error of Estimate is 0.02 for this sample, what would be the sample size?

(B)Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate?

(C)What happens to the Maximum Error of Estimate as the sample size gets smaller?

(D)What effect does the answer to C above have to the size of the confidence interval?

4. By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 3.14 seconds.

Answer each of the following (show all work):

(A) How many measurements should be made in order to be 98% certain that the maximum error of estimation will not exceed 1.0 seconds?

(B) What sample size is required for a maximum error of 1.5 seconds?

5. A 99% confidence interval estimate for a population mean was computed to be (44.1, 62.9). Determine the mean of the sample, which was used to determine the interval estimate

6. A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 190 was taken, and the mean amount spent was $234.01. Assuming a standard deviation equal to $35.51, find the 98% confidence interval for µ, the mean for all such families

7. A confidence interval estimate for the population mean is given to be (49.29, 58.07). If the standard deviation is 16.306 and the sample size is 53, answer each of the following (show all work):

(A) Determine the maximum error of the estimate, E.

(B) Determine the confidence level used for the given confidence interval.

1)The mean of the sampling distribution of means is equal to the mean of the population. T-F, and why or why not?

2) In the formula for the Confidence Interval for the Mean, if the Confidence Coefficient, z(α/2) = 1.65, what is the Confidence Level?

Pg. 432

1. Consider a population with µ =67.1 and σ=5.76 .

(A) Calculate the z-score for x̃ = 65.7 from a sample of size 40.

(B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text? Why or why not?

2.Given a level of confidence of 95% and a population standard deviation of 8, answer the following:

(A) What other information is necessary to find the sample size (n)?

(B) Find the Maximum Error of Estimate (E) if n = 59.

3. A sample of 136 golfers showed that their average score on a particular golf course was 82.77 with a standard deviation of 4.54.

Answer each of the following (show all work

and state the final answer to at least two decimal places.):

(A) Find the 99% confidence interval of the mean score for all 136 golfers.

(B) Find the 99% confidence interval of the mean score for all golfers if this is a sample of 90 golfers instead of a sample of 136.

(C) Which confidence interval is smaller and why?

4. Assume that the population of heights of female college students is approximately normally distributed with mean µ of 67.26 inches and standard deviation σ of 5.96 inches. A random sample of 78 heights is obtained. Show all work.

(A) Find the mean and standard error of the x̃ distribution

(B) Find P( x̃ > 67.50)

5. The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.82 inches and a standard deviation of 0.61 inches. Show all work.

(A) What percentage of the grapefruits in this orchard is larger than 5.78 inches?

(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample is greater than 5.78 inches?

6. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 99% confident that her estimate is correct. If the standard deviation is 4.11, how large a sample is needed to get the desired information to be accurate within 0.56 decibels?

Pg.432

1. Consider a normal population with µ = 25 and σ = 7.0.

(A) Calculate the standard score for a value x of 24.

(B) Calculate the standard score for a randomly selected sample of 45 with = 24.

(C) Explain why the standard scores of 24 are different between A and B above.

2. 2. Assume that the mean SAT score in Mathematics for 11th graders across the nation is 500, and that the standard deviation is 100 points. Find the probability that the mean SAT score for a randomly selected group of 150 11th graders is between 513 and 487.

3. Assume that a sample is drawn and z(α/2) = 1.96 and σ = 30. Answer the following questions:

(A)If the Maximum Error of Estimate is 0.02 for this sample, what would be the sample size?

(B)Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate?

(C)What happens to the Maximum Error of Estimate as the sample size gets smaller?

(D)What effect does the answer to C above have to the size of the confidence interval?

4. By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 3.14 seconds.

Answer each of the following (show all work):

(A) How many measurements should be made in order to be 98% certain that the maximum error of estimation will not exceed 1.0 seconds?

(B) What sample size is required for a maximum error of 1.5 seconds?

5. A 99% confidence interval estimate for a population mean was computed to be (44.1, 62.9). Determine the mean of the sample, which was used to determine the interval estimate

6. A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 190 was taken, and the mean amount spent was $234.01. Assuming a standard deviation equal to $35.51, find the 98% confidence interval for µ, the mean for all such families

7. A confidence interval estimate for the population mean is given to be (49.29, 58.07). If the standard deviation is 16.306 and the sample size is 53, answer each of the following (show all work):

(A) Determine the maximum error of the estimate, E.

(B) Determine the confidence level used for the given confidence interval.

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