In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers divided 69 subjects (27 males and 42 females, ages 17 to 25) into three groups. Participants solved a series of six anagrams on different screen colors: blue, red, and neutral. The time taken, in seconds, to solve the anagrams was recorded. For the 23 members of the neutral group, the paper reports [tex]\bar{x} = 11.58[/tex] and [tex]s = 4.37[/tex].

Give a 99% confidence interval (to 2 decimal places) for the mean time in the population from which the subjects were recruited.

The 99% confidence interval for the meantime in the population from which the subjects were recruited is approximately (9.24, 13.92) with two decimal places.

To calculate the 99% confidence interval for the meantime in the population from which the subjects were recruited, we can use the following formula:

Confidence Interval = x ± Z * (s / √n)

Where:

x = sample mean

s = sample standard deviation

n = sample size

Z = Z-score for the desired confidence level (99% confidence level corresponds to a Z-score of approximately 2.576)

Given:

x = 11.58

s = 4.37

n = 23

Confidence level = 99% (Z-score = 2.576)

Substituting the values into the formula:

Confidence Interval = 11.58 ± 2.576 * (4.37 / √23)

Calculating the standard error:

Standard Error (SE) = s / √n = 4.37 / √23 ≈ 0.907

Now, we can calculate the confidence interval:

Confidence Interval = 11.58 ± 2.576 * 0.907

Confidence Interval = 11.58 ± 2.34

Lower bound = 11.58 - 2.34 ≈ 9.24

Upper bound = 11.58 + 2.34 ≈ 13.92

Therefore, the 99% confidence interval for the meantime in the population from which the subjects were recruited is approximately (9.24, 13.92) with two decimal places.

Learn more about confidence intervals here:

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