In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 71 subjects (23 males and 48 females, ages 17 to 25) into three groups. Participants were asked to solve a series of 6 anagrams. One group was presented with the anagrams on a blue screen; one group saw them on a red screen; and one group had a neutral screen. The time, in seconds, taken to solve the anagrams was recorded. The study reports [tex]\bar{x} = 11.41[/tex] and [tex]s = 4.18[/tex] for the times of the [tex]n = 19[/tex] members of the neutral group.

Calculate a 95% confidence interval for the mean time in the population from which the subjects were recruited. Provide your answer to three decimal places.

A 95% confidence interval for the mean time is from _ to _ seconds.

Given that x¯¯¯ = 11.41, s = 4.18, and n = 19, we need to find the critical value from the t-distribution for a 95% confidence level with n-1 degrees of freedom.

Using a t-table or a calculator, we find that the critical value for a 95% confidence level with 18 degrees of freedom is approximately 2.101.

Substituting the values into the formula, we get:

CI = 11.41 ± (2.101 * (4.18 / √19))

Calculating the expression inside the parentheses, we get:

CI = 11.41 ± (2.101 * 0.957)

Calculating the product, we get:

CI = 11.41 ± 2.008

Therefore, the 95% confidence interval for the mean time in the population is approximately 9.402 to 13.418 seconds.

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