Is it worth pursuing a doctoral degree in education if you already have an undergraduate degree? One way to help make this decision is to look at the mean incomes of these two groups. Suppose that 1414 people with bachelor’s degrees in education were surveyed. Their mean annual salary was $34,000$⁢34,000 with a standard deviation of $9100$⁢9100. Sixteen people with doctoral degrees in education were found to have a mean annual salary of $47,000$⁢47,000 with a standard deviation of $5200$⁢5200. Assume that the population variances are not the same. Construct a 95%95% confidence interval to estimate the true difference between the mean salaries for people with doctoral degrees and undergraduate degrees in education. Let Population 1 be the salaries for people with doctoral degrees and Population 2 be the salaries for people with undergraduate degrees. Round the endpoints of the interval to the nearest whole number, if necessary.

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