Question

A sample size of 10, with a mean of 20 and a sample standard

deviation of 5, at 90% confidence, the intervals are:
a. [17.38,19.45]
b. [14.85, 25.14]
c. [12.82, 15.67]
d. [18.23, 19.32]

Answer 1

Without the critical value, we can't calculate the exact 90% confidence interval for the mean, but wider intervals suggest lower confidence levels, while narrower implies higher levels. So, the given option with the wider interval could be suggestive of the correct 90% confidence interval.

Step-by-step explanation:

The confidence interval for a sample mean is a range that estimates the true population mean with a certain level of confidence. This question asks us to determine which set of intervals presents the correct 90% confidence interval for the given sample. The sample has a size of 10, a mean of 20, and a sample standard deviation of 5. To calculate the confidence interval, we would use the formula: sample mean ± (critical value * (sample standard deviation / √sample size)).

Given that we don't have the critical value presented here, we cannot calculate the exact interval. However, we can look at the options to determine the plausibility of each interval based on an understanding that a narrower interval suggests a higher certainty (as in a higher confidence level, like 95%) and a wider interval suggests less certainty (like a 90% confidence level).