IE 3610 Exam 1
A tolerance interval is a statistical interval that captures a fixed proportion of the population values.
False
As the sample size gets large (approaching infinity) the length of a prediction interval on a future observation approaches zero.
False
For a fixed value of the standard deviation, a 95% confidence interval on the population mean will get shorter if the sample size increases.
False
If a 95% confidence interval on the mean has a lower limit of 10 and an upper limit of 15, this implies that 95% of the time the true value of the mean is between 10 and 15.
False
The length of a 95% CI on the proportion p will be longer if p= 0.1 than if p = 0.5.
False
The method of maximum likelihood always results in unbiased estimators.
False
The sample standard deviation is an unbiased estimator of the population standard deviation.
False
The sampling distribution of the sample mean is the t distribution.
False
The variance of the difference between two independent random variables is the difference in the variances of the two individual random variables.
False
For a fixed value of the standard deviation and a fixed sample size, a confidence interval on the population mean will get longer as the level of confidence increases from 96% to 99%.
True
For a fixed value of the standard deviation, a 95% confidence interval on the population mean will get shorter if the sample size increases.
True
If S2 is the sample variance of a random sample of size n from a normal distribution, the random variable has a chi-square distribution with n - 1 degrees of freedom.
True
In a 95% confidence interval the quantity 0.95 = 1 - 0.05 is called the confidence coefficient.
True
The CI on the variance of a normal distribution makes use of the chi-square distribution.
True
The central limit theorem states that the distribution of the mean of independent, identically distributed random variables with finite variance is the normal distribution.
True
The interval can be used as a large-sample confidence interval for the mean regardless of the population distribution so long as the sample size n is at least 40.
True
The length of a confidence interval is a measure of precision of estimation.
True
The mean squared error of a point estimator includes a variance component and a bias component.
True
The method of maximum likelihood is usually the preferred method for finding point estimators because it produces estimators that have good statistical properties.
True
The normal approximation to the binomial can be use to construct a CI on a population proportion.
True
The prediction interval for a future observation from a normal distribution will always be longer than the CI on the mean of the normal distribution.
True
The probability distribution of a statistic is called a sampling distribution.
True
The quantity has a t-distribution with n - 1 degrees of freedom if the sample mean is computed from a random sample of size n from a normal distribution.
True
The sample mean and sample variance are unbiased estimators of the corresponding population parameters.
True
The sample mean is a moment estimator of the population mean
True
The sample mean is the maximum likelihood estimator of the mean in the normal distribution.
True
The sample size required for constructing a CI on a population proportion that has a specified error n estimation depends on the unknown proportion, p.
True
The standard error of a point estimator is a measure of the precision of the estimation.
True
A t-CI on the mean will be the same length as a z-CI on the mean if the sample standard deviation is equal to the population standard deviation
false
As the sample size gets large (approaching infinity) the length of a CI on the mean approaches the length of the prediction interval.
false
The statistical interval that contains a stated proportion of the values of a probability distribution is called a confidence interval.
false
equation for sample size when p hat is used as an estimate of p and we are AT LEAST 100(1-alpha)% confident error is less than e
n=(z(alpha/2)/2e)^2
equation for sample size when p hat is used as an estimate of p and we are 100(1-alpha)% confident error is less than e
n=(z(alpha/2)/e)^2(p hat)(q hat)
A statistic is a function of observations.
True
All of the observations in a random sample are independent.
True
As the standard deviation increases the sample size required for a fixed length confidence interval on the mean increases.
True
tolerance interval
(sample mean-ks, sample mean+ks)
A point estimator of an unknown parameter is unbiased if the expected value of the estimator equals the parameter.
True
width for prediction interval
w=t(alpha/2)*s*sqrt(1+1/n)
