5. The State of Wisconsin is interested in the performance of its eighth-grade students on the standardizec eighth-grade mathematics assessment test. A research team, tasked by the State, obtains a random samp of 101 eighth-grade student scores and finds that the sample mean is 265 and the sample standard deviation is 55. The scores are approximately normally distributed. (a) Construct a 95% confidence interval for the mean test score in the population of Wisconsin eigh graders and fully interpret your result. (b) The national average on this standardized eighth-grade mathematics assessment test is 260. Base on the available data from Wisconsin (as described above), would you conclude that the average performance of Wisconsin students is significantly different from the average national performance? Explain.

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6. The State of Wisconsin is interested in the performance of its eighth-grade students on the standardized
eighth-grade mathematics assessment test. A research team, tasked by the State, obtains a random sample
of 101 eighth-grade student scores and finds that the sample mean is 265 and the sample standard
deviation is 55. The scores are approximately normally distributed.
(a) Construct a 95% confidence interval for the mean test score in the population of Wisconsin eighth-
graders and fully interpret your result.
(b) The national average on this standardized eighth-grade mathematics assessment test is 260. Based
on the available data from Wisconsin (as described above), would you conclude that the average
performance of Wisconsin students is significantly different from the average national
performance? Explain.
Transcribed Image Text:6. The State of Wisconsin is interested in the performance of its eighth-grade students on the standardized eighth-grade mathematics assessment test. A research team, tasked by the State, obtains a random sample of 101 eighth-grade student scores and finds that the sample mean is 265 and the sample standard deviation is 55. The scores are approximately normally distributed. (a) Construct a 95% confidence interval for the mean test score in the population of Wisconsin eighth- graders and fully interpret your result. (b) The national average on this standardized eighth-grade mathematics assessment test is 260. Based on the available data from Wisconsin (as described above), would you conclude that the average performance of Wisconsin students is significantly different from the average national performance? Explain.
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