1. A researcher wished to compare the average Regents Examination scores achieved by examinees across two different counties in New York. The researcher obtained a simple random sample of 100 test results from Dutchess County and found the mean score to be 88 points with a standard deviation of 8 points. The researcher also obtained an independent simple random sample of 200 test scores of Orange County's examinees and found the mean score to be 83 points with a standard deviation of 10 points. Letm₁ andm₂ represent the mean score by the populations of all examinees in Dutchess County and Orange County, respectively. Assume two-sample tprocedures are safe to use.
   1. What is the 95% confidence interval form₁ -m₂? Interpret your confidence interval in words.
   2. Based on your answer in part (a), would you reject the null hypothesis that the true mean test score is equal between the two groups versus the two-sided alternative at the 5% significance level? Briefly explain.