1. If the sampled population has a mean 48 and standard deviation 18, then the mean and the standard deviation for the sampling distribution of X (X-bar) for n=9 are:
A. 48 and 18
B. 48 and 9
C. 48 and 6
D. 16 and 3
E. 48 and 3
2. 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 more than 94 lbs. is:
A. 34.13%
B. 15.87%
C. 84.13%
D. 56.36%
E. 16.87%
3. Whenever the population has a normal distribution, the sampling distribution of X is normal:
A. For only large sample sizes
B. For only small sample sizes
C. For any sample size
D. Only for samples of size 30 or more
4. 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
5. In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process: What is the probability the mean length of the bolt is more than 3.16 inches?
A. 5.48%
B. 97.72%
C. 94.52%
D. 44.52%
E. 2.28%
6. In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process: What is the probability the mean length of the bolt is less than 3.1 inches?
A.84.13%
B. 100%
C. 71.57%
D. 28.43%
E. 15.87%
7. The width of a confidence interval will be:
A. Narrower for 99% confidence than 95% confidence
B. Narrower for a sample size of 100 than for a sample size of 50
C. Wider for 90% confidence than 95% confidence
D. Wider when the sample standard deviation (s) is small than when s is large
8. A confidence interval increases in width as
A. The level of confidence decreases
B. N increases
C. S decreases
D. All of the above
E. None of the above
9. As standard deviation increases, the samples size has to _____________ to achieve a specified level of confidence.
A. Decrease
B. Increase
C. Remain the same
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 ______________ a confidence interval for a population mean based on a sample of n=150.
A. Wider than
B. Narrower than
C. Equal to
11. When a confidence interval for a population proportion is constructed for a sample size n= 60 and the value of p = 0.4, the interval is based on:
A. The Z distribution
B. The t distribution
C. A Skewed distribution
D. None of the above
12. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a variance of .09. What is the 90% confidence interval for the true mean length of the bolt?
A. 2.8355 to 3.1645
B. 2.5065 to 3.4935
C. 2.8140 to 3.1860
D. 2.4420 to 3.5580
E. 2.9442 to 3.0558
13. 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 99% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company?
A. .1608 to .2392
B. .1992 to .2008
C. .1671 to .2329
D. .1485 to .2515
E. .1714 to .2286
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 4.5, 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. 64 golfers played the hole with the new placement on that day. Determine the probability of the sample average number of strokes is more than 4.3.
2. Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of 0.24 ounces. The weights of the sugar bags are normally distributed. What is the probability that 16 randomly selected packages will have an average weight less than15.97 ounces?
3. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.98 inches. A sample of 49 metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 29.93 and 30.33 inches long?
4. A sample of 25 items yields X (X-bar) =60 grams and s=9 grams. Assuming a normal parent distribution, construct a 99 percent confidence interval for the population mean weight.
5. Of a random sample of 900 trucks at a bridge, 360 had bad signal lights. Construct a 99percent confidence interval for the percentage of trucks that had bad signal lights.
6. Suppose that 80 percent of the voters in a particular region support a candidate. Find the probability that a sample of 1600 voters would yield a sample proportion in favor of the candidate within 1percentage points of the actual proportion.