Final answer:
The 95% confidence interval for the difference in mean brushing times between men and women, given a known standard deviation and equal sample sizes, does not match any of the options provided. After calculation, the correct interval was found to be approximately (-0.86444, 0.46444).
Step-by-step explanation:
The subject of this question is Mathematics, specifically within the field of statistics and probability, as it pertains to conducting hypothesis tests and constructing confidence intervals based on sample data.
To solve this problem, we will use the formula for a two-sample z-confidence interval for the difference between means, because the standard deviation is known. The formula is given by:
(x1 - x2) ± Z* (σ √ (1/n1 + 1/n2))
Where x1 and x2 are the sample means, n1 and n2 are the sample sizes (both 20 in this case), σ is the population standard deviation (1.2), and Z* is the Z-value corresponding to the desired confidence level (1.96 for 95% confidence).
Substituting the values into the formula gives:
(3.6 - 3.8) ± 1.96 * (1.2 √ (1/20 + 1/20))
Calculating this yields an interval of:
(-0.2) ± 1.96 * 0.339
(-0.2) ± 0.66444
So our 95% confidence interval for the difference in mean brushing times between men and women is (-0.86444, 0.46444).
However, this result does not exactly match any of the provided options, suggesting there may have been a miscalculation, a typo in the question's options, or possibly additional context needed. If all calculations are accurate and the context is complete, none of the provided options (A, B, C, D) would be correct.