stats exam 3

A sample of 25 is drawn from a normal population with an unknown population standard deviation. The sample mean and the sample standard deviation are calculated as 35 and 100, respectively. For a 95% confidence interval z0.025=1.96 and t0.025,24=2.064. A 95% confidence interval for the population mean is equal to

35±2.06410025√10025.

Suppose the standard error of xx is 0.10 and s = 0.30. The sample size must be

9

Suppose we use the same data set to construct a 95% tolerance interval and a 95% confidence interval. Consider the relative lengths of the intervals.

The confidence interval will be shorter.

How do the t and z distributions differ?

The t distribution has broader tails (it is flatter around zero).

Suppose you are interested in designing a medical device that will fit comfortably on the wrists of 99% of all adult patients. To do this, should you be interested in a 99% tolerance interval for wrist sizes or a 99% confidence interval for the mean wrist size?

Tolerance interval

The standard error of xx is NOT affected by the

confidence level.

Each t distribution is identified by its

degrees of freedom.

When constructing a confidence interval for the population mean when the population standard deviation is unknown, the degrees of freedom for the t distribution are defined as

n - 1.

The parameter ____ represents the proportion of successes in a population and the statistic _____ represents the proportion of successes in a sample.

p, pˆ

When estimating the population mean, the t distribution is used when the

population variance is unknown.

The standard error is equivalent to ______

s/n

As the degrees of freedom increase, the t distribution becomes more ______ a standard normal distribution.

similar to

If repeated samples of size n are taken from a normal population with an unknown variance, then the statistic ______ follows the t distribution with n-1 degrees of freedom.

t=x⎯⎯−μs/n√

When the confidence level increases from 95% to 99%, the confidence interval for the population mean ________. Multiple choice question.

widens

The value of t.50 is

0

Suppose you choose a sample of size 16 from a normal population and find xx =1.55 and s =0.44. The standard error of xx equals

0.11