Bstats
The expression zα denotes the z-score with an area of _______ to its left.
1-a
A sample is large if it is greater than or equal to
30
A sample is small if it is less than
30
Will the sampling distribution of x always be approximately normally distributed? Explain
No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.
Explain what is meant by the statement, "We are 95% confident that an interval estimate contains μ."
The statement reflects the confidence in the estimation process rather than in the particular interval that is calculated from the sample data. It explains that over many repetitions of this application using the same procedure, 95% of the resulting intervals will contain μ
Will a large-sample confidence interval be valid if the population from which the sample is taken is not normally distributed? Explain
Yes. As long as a sample is sufficiently large that the Central Limit Theorem applies, the confidence interval will be valid regardless of the shape of the population distribution
The expression zα denotes the z-score with an area of _______ to its right.
a
The expression zα/2 denotes the z-score with an area of _______ to its right
a/2
The margin of error is _____________ the width of the confidence interval.
half
Why does sample size need to be accounted for in the t-distribution
he t-distribution changes for different sample sizes
The more variable the data, the _______ accurate the sample mean will be as an estimate of the population mean
less
The larger the sample, the _______ accurate the sample mean will be as an estimate of the population mean.
more
A single number calculated from the sample that estimates a target population parameter is called a _____ estimator. A _____ estimator is a range of numbers that contain the target parameter with a high degree of confidence
point; interval
hen the population standard deviation is not known, what is used to estimate it
the standard deviation of the data from the sample
T/F: If x is a good estimator for μ, then we expect the values of x to cluster around μ
true
T/F: In most situations, the true mean and standard deviation are unknown quantities that have to be estimated
true
T/F: The Central Limit Theorem guarantees an approximately normal sampling distribution for the sample mean for large sample sizes, so no knowledge about the distribution of the population is necessary for the corresponding interval to be valid.
true
T/F: The confidence level is the confidence coefficient expressed as a percentage
true