Answer :
(a) the 95% confidence interval for the mean time in the population is approximately (9.795, 13.365) seconds.
(a) To calculate a 95% confidence interval for the mean time in the population from which the subjects were recruited, we can use the formula for the confidence interval:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation of the Sample / √Sample Size)
Given the information provided, we have:
- Sample Mean = 11.58 (mean time for the neutral group)
- Sample Standard Deviation (s) = 4.37 (standard deviation for the neutral group)
- Sample Size (n) = 23 (members of the neutral group)
We need to find the critical value corresponding to a 95% confidence level. Since the sample size is relatively large (n > 30), we can use the Z distribution. The critical value for a 95% confidence level is approximately 1.96.
Substitute the values into the formula:
Confidence Interval = 11.58 ± 1.96 * (4.37 / √23)
Calculating the values:
Confidence Interval ≈ 11.58 ± 1.96 * 0.913
Confidence Interval ≈ (9.795, 13.365)
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The complete question is :
In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 69 subjects (27 males and 42 females ranging in age from 17 to 25 years) into three groups. Participants were asked to solve a series of six 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 paper reporting the study gives = 11.58 and s = 4.37 for the times of the 23 members of the neutral group
(a)Give a 95% confidence interval for the mean time in the population from which the subjects were recruited.
