The average math SAT score is 521 with a standard deviation of 114. A particular high...

The average math SAT score is 521 with a standard deviation of 114. A particular high school claims that its students have unusually high math SAT scores. A random sample of 60 students from this school was selected, and the mean math SAT score was 538. Is the high school justified in its claim? Explain.

answers is ( choose yes/or no) , because the z score ( which is? ) is ( choose, usual or not usual) since it ( choose, does not lie ,or lies) within the range of a usual event , namely within ( choose 1, 2 or 3 standard deviations) of the mean of the sample means. round to two decimal places as needed

Solutions

Expert Solution

Let X be the SAT score of any given student. X has a mean and standard deviation

Note that we do not know the distribution of X

Let be the sample means of a randomly selected sample of n=60 students. Since the sample size is greater than 30, using the central limit theorem (CLT), we can say that has a normal distribution with mean and standard deviation (also called standard error of mean)

A random sample of size 60 selected from this particular school has a mean SAT score of 538.

The z score of 538 is

We can see that any random sample of 60 students would have a sample mean SAT score of 521 with SD 14.7173. This particular school had a sample mean of 538 which is 1.16 standard deviation from the mean. We say that a value which is more than 2 standard deviations from the mean is unusual. Hence this score is not unusual.

Is the high school justified in its claim that its students have unusually high math SAT scores?

ans: No, because the z score 1.16 is not usual since it lies within the range of a usual event , namely within 2 standard deviations of the mean of the sample means.

orchestra answered 1 year ago

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