Question

# A random sample of n individuals were selected. A 95% confidence interval (\$52,000 to \$70,000) was...

A random sample of n individuals were selected. A 95% confidence interval (\$52,000 to \$70,000) was constructed using the sample results.

Which of the following statement(s) is/are true? ( Can choose more than one answer)

If all possible samples of size n were drawn from this population, about 95% of the population means would fall in the interval (\$52,000 to \$70,000).

We do not know for sure whether the population mean is in the interval \$52,000 and \$70,000.

If all possible samples of size n were drawn from this population, 95% of the intervals established by the above method would contain the population mean.

If all possible samples of size n were drawn from this population, about 95% of the sample means would fall in the interval (\$52,000 to \$70,000).

Correct options:

We do not know for sure whether the population mean is in the interval \$52,000 and \$70,000.

If all possible samples of size n were drawn from this population, 95% of the intervals established by the above method would contain the population mean.

Explanation:

Initerpretation of Confidence Interval:

A 95% confidence interval (\$52,000 to \$70,000) is a range of values we can be 95% certain contains the unknown true mean of the population.

If repeated samples are taken and the 95% confidence interval is computed for each sample, 95% of the intervals will contain the population mean.

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