# statistics A sample size of 900 is not large enough to conclude

January 30, 2017

Question
Assignment-3: (Chs. 7 and 8): Due by Midnight of Sunday, March 3 2013: Total 70 points (must show work where possible)

True/False (1 point each)

Chapter 7
1 A sample size of 900 is not large enough to conclude that the sampling distribution of p is a normal distribution, when the estimate of the population proportion is 0.995.

2 .The standard deviation of all possible sample proportions increases as the sample size increases.

3.For any sampled population, the population of all sample means is normally distributed.

4. The mean of the sampling distribution of 12X”> is always equal to the mean of the sampled population.

5.The reason sample variance has a divisor of n-1 rather than n is that it makes the standard deviation an unbiased estimator of the population standard deviation.

Chapter 8
6. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval without the finite population correction factor is wider than the confidence interval with the finite population correction factor.

7. When the population is normally distributed and the population standard deviations is unknown, then for any sample size n, the sampling distribution of 12X”> is based on the t distribution.

8. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 200 will be wider than a confidence interval for a population mean based on a sample of n = 150.

9. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be wider, when the sample standard deviation s is small than when s is large.

10. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be narrower than a confidence interval for a population mean based on a sample of n = 50.

11.The sample mean, the sample proportion and the sample standard deviation are all unbiased estimators of the corresponding population parameters.

12.Assuming the same level of significancea, as the sample size decreases, the value of ta/2 approaches the value of za/2.

Multiple Choices (2 points each)
Chapter 7
1. A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will be less than 94 lbs. is:
A. 15.87%
B. 84.13%
C. 34.13%
D. 56.36%
E. 16.87%

2 The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 13 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that no more than 40 accounts will be classified as delinquent?
A. 42.07%
B. 92.07%
C. 7.93%
D. 40.15%
E. 90.15%

3. If we have a sample size of 100 and the estimate of the population proportion is 0.10, the mean of the sampling distribution of the sample proportion is:
A. 0.009
B. 0.10
C. 0.03
D. 0.90
E. 0.09

4. Consider a sampling distribution formed based on n = 10. The standard deviation of the population of all sample means 12ÏƒX “> is ______________ more than the standard deviation of the population of individual measurementss.
A. Always
B. Sometimes
C. Never

5. A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will be be less than 84 lbs. is:
A. 16.87%
B. 93.32%
C. 43.32%
D. 6.68%
E. 84.13%

6. If a population distribution is known to be normal, then it follows that:
A. The sample mean must equal the population mean
B. The sample mean must equal the population mean for large samples
C. The sample standard deviation must equal the population standard deviation
D. All of the above
E. None of the above

7.According to a hospital administrator, historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospital patients has just been conducted. Sixty-four (64) patients indicated that they were dissatisfied with the after surgery care. What are the mean and the standard deviation of the sampling distribution of p?
A. 16% and .034%
B. 20% and 1.83%
C. 20% and 2%
D. 20% and .034%
E. 20% and 16%

Chapter 8

8. The width of a confidence interval will be:
A. Narrower for 95% confidence than 99% confidence
B. Wider for a sample size of 100 than for a sample size of 50
C. Wider for 90% confidence than 95% confidence
D. Narrower when the sample standard deviation (s) is large than when s is small

9. When the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be __________ when p(1-p) is larger than when p(1-p) is smaller.
A. Narrower
B. Wider
C. Neither A nor B, they will be the same
D. Cannot tell from the information given

10. A confidence interval increases in width as
A. The level of confidence increases
B. n decreases
C. s increases
D. All of the above
E. None of the above

11.In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 95% confidence interval for the true mean length of the bolt?
A. 2.804 to 3.196
B. 2.308 to 3.692
C. 2.769 to 3.231
D. 2.412 to 3.588
E. 2.814 to 3.186

12. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). For this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. What is the 95% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company?
A. 0.1485 to 0.2515
B. 0.1608 to 0.2392
C. 0.1992 to 0.2008
D. 0.1671 to 0.2329
E. 0.1714 to 0.2286

13. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are current (between 0 and 60 days after billing). The historical records show that over the past 8 years 70 percent of the accounts have been current. Determine the sample size needed in order to be 95% confident that the sample proportion of the current customer accounts is within .02 of the true proportion of all current accounts for this company.
A. 1421
B. 1549
C. 1842
D. 2017
E. 3484

14. A company is interested in estimating the mean number of days of sick leave taken by its employees. The firm’s statistician randomly selects 200 personnel files and notes the number of sick days taken by each employee. The estimated sample mean is 12.2 days and the sample standard deviation is 10 days. How many personnel files would the director have to select in order to estimatem to within 1 day with a 99% confidence interval?
A. 166
A. 200
B. 385
C. 550
E. 664

Essay Type (show your work) (5 points each)
Chapter 7

1. A PGA (Professional Golf Association) tournament organizer is attempting to determine whether hole (pin) placement has a significant impact on the average number of strokes for the 13th hole on a given golf course. Historically, the pin has been placed in the front right corner of the green and the historical mean number of strokes for the hole has been 4.25, with a standard deviation of 1.6 strokes. On a particular day during the most recent golf tournament, the organizer placed the hole (pin) in the back left corner of the green. 49 golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes more than 4.55.

2. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.27 inches. A sample of 9 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.23 and 30.32 inches long?

3. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.18 ounces. The weights of the sugar bags are normally distributed. What is the probability that 36 randomly selected packages will have average weight less than 15.955 ounces?

Chapter 8

4. A small town has a population of 20,000 people. Among these 1,000 regularly visit a popular local bar. A sample of 100 people who visit the bar is surveyed for their annual expenditures in the bar. It is found that on average each person who regularly visits the bar spends about \$2000 per year in the bar with a standard deviation of \$200. Construct a 99 percent confidence interval around the mean annual expenditure in the bar.

5. The production manager for the XYZ manufacturing company is concerned that the customer orders are being shipped late. He asked one of his planners to check the timeliness of shipments for 1000 orders. The planner randomly selected 1000 orders and found that 100 orders were shipped late. Construct the 99% confidence interval for the proportion of orders shipped late.

6. The weight of a product is measured in pounds. A sample of 49 units is taken from a batch. The sample yielded the following results: 12X”> = 80 lbs. and s = 10.5 lbs. Calculate a 90 percent confidence interval for the mean.

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