IE 3610 Exam 1

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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)


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