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