Determine the point estimate for the difference in mean standardized scores for the eastern and western sides of the state, ?1 − ?2. (b) Calculate the margin of error for a 98% confidence interval. (Use a table or technology. Round your answer to four decimal places.) (c) Interpret the point estimate and margin of error in the context of the problem. The sample data estimate the difference in standardized scores of the eastern and western sides of the state to be with a margin of error, rounded to four decimal places, of at the 98% confidence level.
In the United States, standardized testing is used to compare students' knowledge retention across the country. States will often use the results of standardized testing to allocate funding to districts within the state. One state in particular wanted to determine whether there was a difference in scores between schools on the eastern side of the state and schools on the western side of the state. A random sample of 30 schools on the eastern side and 35 schools on the western side were chosen. The mean score for the eastern schools was
with a standard deviation of 5.3. The mean score for the western schools was
with a standard deviation of 4.4. We would like to estimate the difference in the mean standardized scores from the eastern schools and western schools and determine the margin of error of this estimate with 98% confidence.
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