stats exam 3

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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.
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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√
How do the t and z distributions differ?
The t distribution has broader tails (it is flatter around zero).
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.
As the degrees of freedom increase, the t distribution becomes more ______ a standard normal distribution.
similar to
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.
Each t distribution is identified by its
degrees of freedom.
The standard error is equivalent to ______
s/n
When the confidence level increases from 95% to 99%, the confidence interval for the population mean ________.
Multiple choice question.
widens
When estimating the population mean, the t distribution is used when the
population variance is unknown.
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.
The standard error of xx is NOT affected by theconfidence level.The value of t.50 is0Suppose 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 equals0.11Suppose 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 intervalSuppose the standard error of xx is 0.10 and s = 0.30. The sample size must be9The parameter ____ represents the proportion of successes in a population and the statistic _____ represents the proportion of successes in a sample.p, pˆ