Final answer:
To be 95% confident that the sample variance is within 20% of the population variance, we need to calculate the margin of error using the z-score, sample variance, and sample size. If the margin of error is less than 20% of the sample variance, then we can be 95% confident that the population variance is within 20% of the sample variance.
Step-by-step explanation:
To be 95% confident that the sample variance is within 20% of the population variance, we need to calculate the margin of error. The margin of error is determined by multiplying the critical value (z-score) with the standard deviation. In this case, since the population variance is unknown, we can use the sample variance as an estimate. We can then calculate the margin of error using the formula: Margin of Error = (z * sqrt(sample variance)) / sqrt(sample size).
Once we have the margin of error, we can determine the range within which the population variance will be based on the 20% threshold. If the margin of error is less than 20% of the sample variance, then we can be 95% confident that the population variance is within 20% of the sample variance.
Therefore, the answer to the question is 2) No, we cannot be 95% confident that the sample variance is within 20% of the population variance.