In a randomized comparative experiment on the effect of color on the performance of a cognitive task, researchers randomly divided 65 subjects (30 males and 35 females ranging in age from 17 to 25 years) into three groups. Participants were asked to solve a series of 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 -11.73 and 4.41 for the times of the 19 members of the neutral group.

Provide your answer to the following question, giving it to three decimal places: What is a 98% confidence interval for the mean time in the population from which the subjects were recruited?

The 98% confidence interval for the mean time can be calculated by first calculating the sample mean and standard deviation, then using these values with the critical value from a statistical table at the 98% confidence level to find lower and upper limits of the interval in which the real population mean is expected to be found.

This question requires a solid understanding of statistics, particularly in estimating the population mean from a given sample data. Given the data (times of the 19 members of the neutral group), the aim is to calculate the 98% confidence interval for the mean time taken to solve the anagrams for the entire population from which the subjects were chosen.

A confidence interval is a type of interval estimate that is likely to contain the population parameter. In this case, the parameter of interest is the mean time taken to solve the anagrams. To calculate the 98% confidence interval, one would firstly need to find out the sample mean and sample standard deviation. Afterwards, you would use a suitable statistical table (likely the t-distribution table as we do not know the population standard deviation) to find the critical value at 98% level of confidence.

Once these values are known, the confidence interval can be calculated using this formula: (sample mean - (critical value * standard deviation / sqrt(sample size)), sample mean + (critical value * standard deviation / sqrt(sample size))). The result will be the lower and upper limit of the interval estimate, giving the range of values within which we can be 98% confident that the actual population mean lies.

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