The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 0 to 500 . Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot. In 2015, 136,900 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was ?¯=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 ?=110 . (a) 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? (Enter your answer rounded to four decimal places.) standard deviation = (b) 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 ? ? (Enter your answer rounded to four decimal places.) points = (c) What is the 95% confidence interval for the population mean score ? based on this one sample? (Enter your answer rounded to one decimal place.) Lower value = Higher value =
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test
In 2015, 136,900 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was ?¯=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 ?=110 .
(a) If we take many samples, the sample mean ?¯ varies from sample to sample according to a
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