SBZRO
10-02-2007, 04:49 PM
Well, I got a take home test thats due in an hour and a half. I hate business statistics, so I was wondering if anybody could help me out.
1. An accounting firm’s planning assumption is that in the long run, their non-CPA members will average 1,550 chargeable hours per year. Some members of the firm were concerned that chargeable hours were below plan in 2006. In 2006, the 16 non-CPA members charged an average of 1,531.4 hours, with a sample standard deviation of 239.6 hours.
a. Assume that for 2006 the mean for chargeable hours was indeed 1,550 hours as planned. Determine the probability of observing a sample mean of 1,531.4 or lower due to random sampling error.
2. Based on your result in part a, do the data provide a convincing reason to believe that the mean was discernibly lower than planned?The marketing plan for a new product assumes that 50% of current customers will switch to the new product in the first year after its introduction.
a. Suppose you were to survey a random sample of 200 current customers one year after the introduction. Assuming the plan is correct, determine the probability that 46% or fewer of the surveyed customers would report that they had switched to the new product in the first year.
b. Suppose that you carried out the survey described in part a, and found that indeed 46% of the surveyed customers had switched to the new product in the first year. In light of your answer in part a, what would you conclude about the plan?
3. The following are the lifetimes (in hours) of a random sample of a type of electrical component: 142.84, 97.04, 32.46, 69.14, 85.67, 114.43, 41.76, 163.07, 108.22, and 63.28. Assume the distribution of component lifetimes is reasonably close to a normal distribution.
a. Determine a 98% confidence interval for μ.
b. In part a, approximately how large a sample would be required to achieve a margin of sampling error of 20 hours? Hint: Use an estimate of σ in Expression (6.5).
4. An auditor takes a random sample of size n = 36 from a population of 10,000 accounts receivable. The population mean is μ = $250 with population standard deviation σ = $40.
a. What is the probability that the sample mean will be less than $230?
b. What is the probability that the sample mean will be greater than $290?
c. What is the probability that the sample mean will be within $20 of the population mean?
5. It has been observed over the years that 8% of all shipments of machine parts are defective. If a random sample of 100 parts is selected, determine:
a. The mean and the standard deviation of the sample proportion p of defective parts.
b. Determine a above for a random sample of 200 parts.
c. Based on your results in a and b, how does the sample size affect the mean and the standard error of p?
1. An accounting firm’s planning assumption is that in the long run, their non-CPA members will average 1,550 chargeable hours per year. Some members of the firm were concerned that chargeable hours were below plan in 2006. In 2006, the 16 non-CPA members charged an average of 1,531.4 hours, with a sample standard deviation of 239.6 hours.
a. Assume that for 2006 the mean for chargeable hours was indeed 1,550 hours as planned. Determine the probability of observing a sample mean of 1,531.4 or lower due to random sampling error.
2. Based on your result in part a, do the data provide a convincing reason to believe that the mean was discernibly lower than planned?The marketing plan for a new product assumes that 50% of current customers will switch to the new product in the first year after its introduction.
a. Suppose you were to survey a random sample of 200 current customers one year after the introduction. Assuming the plan is correct, determine the probability that 46% or fewer of the surveyed customers would report that they had switched to the new product in the first year.
b. Suppose that you carried out the survey described in part a, and found that indeed 46% of the surveyed customers had switched to the new product in the first year. In light of your answer in part a, what would you conclude about the plan?
3. The following are the lifetimes (in hours) of a random sample of a type of electrical component: 142.84, 97.04, 32.46, 69.14, 85.67, 114.43, 41.76, 163.07, 108.22, and 63.28. Assume the distribution of component lifetimes is reasonably close to a normal distribution.
a. Determine a 98% confidence interval for μ.
b. In part a, approximately how large a sample would be required to achieve a margin of sampling error of 20 hours? Hint: Use an estimate of σ in Expression (6.5).
4. An auditor takes a random sample of size n = 36 from a population of 10,000 accounts receivable. The population mean is μ = $250 with population standard deviation σ = $40.
a. What is the probability that the sample mean will be less than $230?
b. What is the probability that the sample mean will be greater than $290?
c. What is the probability that the sample mean will be within $20 of the population mean?
5. It has been observed over the years that 8% of all shipments of machine parts are defective. If a random sample of 100 parts is selected, determine:
a. The mean and the standard deviation of the sample proportion p of defective parts.
b. Determine a above for a random sample of 200 parts.
c. Based on your results in a and b, how does the sample size affect the mean and the standard error of p?