If we take many samples, the sample mean ?⎯⎯⎯�¯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score ?� in the population. What is the standard deviation of this sampling distribution? Give your answer to four decimal places. What is the standard deviation ? According to the 95 part of the 68-95-99.7 rule, 95%of all values of ?⎯⎯⎯�¯ fall within how many points on either side of the unknown mean ??�? Give your answer to four decimal places. What are the points? Use the 95 part of the 68-95-99 rule to determine a 95% confidence interval for the population mean score ?� based on this one sample. Give your answers to at least two decimal places. What is the lower bound ? What is the upper bound ?
The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test
In 2019, 147,400 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was ?⎯⎯⎯=282.�¯=282. We want to estimate the mean score ?� in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation ?=40.
If we take many samples, the sample mean ?⎯⎯⎯�¯ varies from sample to sample according to a
Give your answer to four decimal places.
According to the 95 part of the
Use the 95 part of the 68-95-99 rule to determine a 95% confidence interval for the population mean score ?� based on this one sample. Give your answers to at least two decimal places.
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