Question

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).

Answer 1

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.