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