Exam 7: Estimation: Single Population

The width of a confidence interval is equal to twice the margin of error.

In a survey of 472 personnel directors,63% thought that they would be hiring new personnel over the next three months.Which of the following represents a 98% confidence interval for the proportion of all personnel directors planning to hire personnel over the next three months?

Find the upper confidence limit of the 99% confidence interval.

If a sample of size 21 is selected,the value of A for the probability P(t ≥A)= 0.025 is:

The value of the standard error of the mean is determined by dividing the total error by the sample size.

If the shopping times for a random sample of 25 shoppers in a supermarket are normally distributed with a known population standard deviation of 15 minutes,the standard error is equal to 0.6.

The lower limit of a 95% confidence interval for the population proportion P given a sample size n = 100 and sample proportion = 0.62 is equal to:

The Student's t distribution is the ratio of the standard normal distribution to the square root of the chi-square distribution divided by its degrees of freedom.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A clinic offers a weight-reduction program.A review of its records revealed the following weight losses,in pounds,for a random sample of 10 of its clients at the conclusion of the program: 20,15,21,28,22,19,9,14,18,and 23. -Without doing any calculations,explain whether a 90% confidence interval for the population mean would be wider than,narrower than,or the same as that of a 95% confidence interval for the population mean.

An estimator is unbiased if the mean of its sampling distribution is the population parameter being estimated.

An unbiased estimation procedure for the population total Nμ yields the point estimate N .

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random sample of ten homes in a particular suburb had the following selling prices (in thousands of dollars): 92,83,110,115,108,96,102,90,100,and 98. -Use an unbiased estimation procedure to find a point estimate of the variance of the sample mean.

Find the lower confidence limit of the 90% confidence interval.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A computer is programmed to draw 1000 samples,each of size 40 from a normally distributed population having mean 50 and standard deviation 10.For each sample,the mean and the median are computed.The average value and standard deviation of each set of estimates for the 1000 samples are as follows. -Which statistic appears to be more efficient?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A process producing bricks is known to produce bricks whose weights are normally distributed with a standard deviation of 0.11 lb.A random sample of 16 bricks from today's output had a mean weight of 4.08 lb. -It is decided that tomorrow a sample of 20 bricks will be taken.Without doing the calculations,explain whether a correctly calculated 95% confidence interval for the mean weight of tomorrow's output would be wider than,narrower than,or the same width as that of a 99% confidence interval for the mean weight of all bricks produced this day.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A regional CPA firm conducted an audit for a discount chain.One part of the audit involved developing an estimate for the mean dollar error in total charges that occur during the checkout process.They wish to develop a 90% confidence interval estimate for the population mean.A simple random sample of n = 20 is selected,with the following data (in dollars): -The number of television sets coming off a production line each day is known to have a standard deviation of 17.4 sets per day.The production line averaged 852.3 sets per day for 20 randomly selected days.What is the level of confidence associated with the interval 844.75 to 860.0?

If the campaign manager of a US senator is interested in estimating the proportion of registered voters who will support the senator during the next election,the sample proportion would be the appropriate point estimate.

The probability density functions of normal distributions and t distributions are symmetric about their means.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A process producing bricks is known to produce bricks whose weights are normally distributed with a standard deviation of 0.11 lb.A random sample of 16 bricks from today's output had a mean weight of 4.08 lb. -Suppose that the population standard deviation for today's output is 0.14 lb (not 0.11 lb).Without doing the calculations,explain whether a correctly calculated 99% confidence interval for the mean weight of today's output would be wider than,narrower than,or the same width as that of a 99% confidence interval calculated using the population standard deviation of 0.11 lb for today's output.

A 95% confidence interval estimate for a population mean μ is determined to be 62.8 to 73.4.If the confidence level is reduced to 90%,the confidence interval for μ becomes narrower.