(21.23) A study of the effect of exposure to color (red or blue) on the ability to solve puzzles used 42 subjects. Half the subjects (21) were asked to solve a series of puzzles while in a red-colored environment. The other half (21) were asked to solve the same series of puzzles while in a blue-colored environment. The time taken to solve the puzzles was recorded for each subject. The 21 subjects in the red-colored environment had a mean time for solving the puzzles of 9.64 seconds with standard deviation 3.43; the 21 subjects in the blue-colored environment had a mean time of 15.84 seconds with standard deviation 8.65. The two-sample t statistic for comparing the population means has value

There is enough statistical evidence to say that the means are different.

Step-by-step explanation:

The question is incomplete:

"The two-sample t statistic for comparing the population means has value (±0.001)."

The null and alternative hypothesis are:

The level of significance is assumed to be α=0.01.

The difference of the sample means is:

The standard deviation for the difference of the means is:

Then, the t-statistic is:

The degrees of freedom are:

With 40 degrees of freedom the t-critial for a significance of α=0.01 is t=±2.705.

As the t-statistic lies in the rejection region, the effect is significant and the null hypothesis is rejected.

There is enough statistical evidence to say that the means are different.