Question

A manufacturer claims that their highlighters could write continuously for 14 hours. A researcher wanted to find out if the highlighters would last longer than 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. The mean was 14.5 hours and the standard deviaton was 1.2 hours.

Find the​ 95% confidence interval for the mean writing time for all the highlighters.
​(round to three decimal​ places)

Answer 1

95% confidence interval for the mean writing time for all the highlighters is approximately 14.055 to 14.945 hours.

Step-by-step explanation:

To find the 95% confidence interval for the mean writing time for all the highlighters, we can use the formula:

Confidence Interval = mean +/- (critical value) * (standard deviation / sqrt(sample size))

Given that the mean is 14.5 hours, the standard deviation is 1.2 hours, and the sample size is 40, we need to find the critical value for a 95% confidence level. Using a t-distribution table or calculator, the critical value is approximately 2.021.

Substituting these values into the formula, the confidence interval is:

Confidence Interval = 14.5 +/- 2.021 * (1.2 / sqrt(40))

Confidence Interval ≈ 14.5 +/- 0.445

Therefore, the 95% confidence interval for the mean writing time for all the highlighters is approximately 14.055 to 14.945 hours.