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One reason for using a tdistribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

(a) zcan be used only for large samples.

(b) zrequires that you know the population standard deviation σ.

(c) zrequires that you can regard your data as an SRS from the population.

(d) the standard Normal table doesn't include confidence levels at the bottom.

(e) a zcritical value will lead to a wider interval than a tcritical value.

Short Answer

Expert verified

(b) z requires that you know the population standard deviation σ.

Step by step solution

01

Given Information

(a) zcan be used only for large samples.

(b) zrequires that you know the population standard deviation σ.

(c) zrequires that you can regard your data as an SRS from the population.

(d) the standard Normal table doesn't include confidence levels at the bottom.

(e) a zcritical value will lead to a wider interval than a tcritical value.

02

Explanation

(a) False, zcan also be used for small samples from a Normal population.

(b) True, if you know the population standard deviation σ, then you use the z-procedure, else you use the t-procedure.

(c) False, a random sample instead of a simple random sample is also sufficient.

(d) False, you can still determine the critical value using the standard Normal table.

(e) False, the procedure to be used is not dependent on the width of the interval.

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