True / False Questions (1 point each) 1. The sampling distribution of X (X-bar) is not always a normal distribution. 2. The reason sample variance has a divisor of n-1 rather than n is that it makes the sample standard deviation an unbiased estimate of the population standard deviation. 3. The standard deviation of the sampling distribution of the sample mean decreases as the sample size increases. 4. If the sampled population is a normal distribution, then the sampling distribution of X (X- bar) may not be normal for a small sample size. 5. The central limit theorem states that as sample size increases, the sampling distribution of the sample mean more closely approximates a normal distribution. 6. If a population is known to be normally distributed, then it follows that the sample mean must equal the population mean. 7. The mean of the sampling distribution of X (X-bar) is always equal to the mean of the sampled population. 8. Assuming the same level of significance, as the sample size increases, the value of t/2 (t- half alpha) becomes larger and larger than the value of Z/2 (Z- half alpha). 9. When constructing a confidence interval for a sample Mean, the t distribution is appropriate whenever the sample size is small. 10. When the population is normally distributed and the population standard deviation is unknown, then for any sample size n, the sampling distribution of X (X-bar) is based on the t distribution. 11. 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 wider than a confidence interval for a population mean based on a sample of n = 150. 12. When the level of confidence and the sample size remain the same, a confidence interval for a population mean will be narrower, when the sample standard deviation s is smaller than when s is larger. 1 Essay type Questions (6 points each) 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 than 15.97 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 99 percent 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 1 percentage points of the actual proportion. 2