The Law School Admission Test (LSAT) is designed so that test scores are normall
ID: 3176436 • Letter: T
Question
The Law School Admission Test (LSAT) is designed so that test scores are normally distributed. The mean LSAT score for the population of all test-takers in 2005 was 154.35 with a standard deviation of 9.75.
From this data, suppose that the LSAT scores discussed were not normally distributed. For a sample size of 10,000, would the sampling distribution of the mean be a normal distribution (5 pts)?
If you drew all possible random samples of size 1,000 from the population of LSAT test takers and plotted the values of the mean from each sample, the resulting distribution would be the sampling distribution of the mean. Would this sampling distribution be a normal distribution? Why or why not? (5 pts)?
If you drew all possible random samples of size 100 from the population of LSAT test takers and plotted the values of the mean from each sample, the resulting distribution would be the sampling distribution of the mean. What is the value of the mean of the sampling distribution (5 pts)?
Please calculate the value of the standard error of the mean for the sampling distribution for 10,000 samples. Explain what the standard error measures or describes about the sampling distribution (5 pts).
Explanation / Answer
The central limit theorem states that for a large sample, where n >30, y bar is approximately normally distributed, regardless of the distribution of the population one samples from. So for a sample size of 10,000, the sampling distribution of the mean will be a normal distribution.
If we drew all possible random samples of size 1,000 from the population of LSAT test takers and plotted the values of the mean from each sample, the resulting distribution would be the sampling distribution of the mean. Yes, this sampling distribution will be a normal distribution. This is because If the population is normally distributed, then the sampling distribution of the sample mean is also normally distributed no matter what the sample size is.
If you drew all possible random samples of size 100 from the population of LSAT test takers and plotted the values of the mean from each sample, the resulting distribution would be the sampling distribution of the mean. The value of the mean of sampling distribution is 154.35. The value of the mean of sampling distribution will be same as the value of the mean of population.
Standard error of the mean for the sampling distribution for 10,000 samples is:
Standard Error = Standard Deviation/n = 9.75/10000
Standard error = 0.0975
Standard error is the standard deviation of the sampling distribution.
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