Exam 8: Confidence Intervals

On a standard IQ test,the standard deviation is 15.How many random IQ scores must be obtained if we want to find the true population mean (with an allowable error of 0.5)and we want 97 percent confidence in the results?

What sample size is needed to estimate with 95 percent confidence the mean intake of daily calcium within 20 units of the true mean if the intake is normally distributed with a variance of 1900 units?

As the stated confidence level decreases,the width of the confidence interval _______________.

A random sample n = 15 is taken from a population assumed to be normal,and = 1.2 and the sample variance is .36.Calculate a 99 percent confidence interval for μ.

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.

When the margin of error is added to and subtracted from the sample mean,an interval is formed that will contain μ with a probability of (1 − α).

A local company makes a candy that is supposed to weigh 1.00 ounces.A random sample of 25 pieces of candy produces a mean of 0.996 ounces with a standard deviation of 0.004 ounces.Construct a 98 percent confidence interval for the mean weight of all such candy.

The state agriculture department tested 203 fuel samples across the state in 2009 for accuracy of the reported octane level.For premium grade,14 out of 105 samples failed.Find a 99 percent confidence interval for the true population proportion of premium grade fuel-quality failures.

A sample of 2,000 people yielded =.52.What is the variance of the population proportion?

You want to estimate the proportion of customers who are satisfied with their experiences at a local supermarket at α = .10 and within .025 of the true value.It has been estimated that p =.85.How large of a sample is needed?

A local company makes a candy that is supposed to weigh 1.00 ounces.A random sample of 25 pieces of candy produces a mean of 0.996 ounces with a standard deviation of 0.004 ounces.How many pieces of candy must we sample if we want to be 99 percent confident that the sample mean is within 0.001 ounces of the true mean?

As the sample size n increases,the width of the confidence interval _______________.

The customer service manager for the XYZ Fastener Manufacturing Company examined 60 invoices and found 9 that contained errors.Find a 98 percent confidence interval for the proportion of invoices with errors.

A local country club golf tournament organizer is attempting to estimate the average number of strokes for the 13th hole.On a particular day,64 players completed the play on the 13th hole,with an average of 4.25 strokes and a population standard deviation of 1.6 strokes.Determine the 95 percent confidence interval for the average number of strokes.

When the level of confidence and sample proportion remain the same,a confidence interval for a population proportion p based on a sample of n = 100 will be ______________ a confidence interval for p based on a sample of n = 400.

If the 95 percent confidence interval for a mean is from .771 to 1.629,can we conclude that μ = .5,using a 95 percent confidence interval?

When the population is normally distributed and the population standard deviation σ is unknown,then for any sample size n,the sampling distribution of is based on the z distribution.

In determining the sample size to estimate a population proportion,as p approaches .5,the calculated value of the sample size ______________.

A sample of 2,000 people yielded =.52.Calculate a 99 percent confidence interval for p.

A sociologist develops a test designed to measure attitudes about disabled people and gives the test to 16 randomly selected subjects.Their mean score is 71.2 with a standard deviation of 10.5.Construct the 99 percent confidence interval for the mean score of all subjects.