The Trial Urban District Assessment (TUDA) is a government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from 0 to 500. A score of 243 is a ”basic” reading level and a score of 281 is ”proficient.” Scores for a random sample of 1400 eighth-graders in Dallas had x = 248 with standard deviation s = 14.525. (a) Urban children often perform below the basic level. At the 5% significance level is there good evidence that the mean for all Dallas eighth-graders is more than the basic level? (b) Find a 99% confidence interval for the mean score of all Dallas eighth-graders. (c) Consider a number line where you have plotted the null hypothesis value and the 99% confidence interval. What do you notice about how the confidence interval relates to the null hypothesis value. Explain why this makes sense in terms of the conclusion from your hypothesis test.
The Trial Urban District Assessment (TUDA) is a government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from 0 to 500. A score of 243 is a ”basic” reading level and a score of 281 is ”proficient.” Scores for a random sample of 1400 eighth-graders in Dallas had x = 248 with standard deviation s = 14.525.
(a) Urban children often perform below the basic level. At the 5% significance level is there good evidence that the mean for all Dallas eighth-graders is more than the basic level?
(b) Find a 99% confidence interval for the mean score of all Dallas eighth-graders.
(c) Consider a number line where you have plotted the null hypothesis value and the 99% confidence interval. What do you notice about how the confidence interval relates to the null hypothesis value. Explain why this makes sense in terms of the conclusion from your hypothesis test.
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