Use the following to answer questions 1-3: Scores on the verbal portion of SAT e

Question

Use the following to answer questions 1-3: Scores on the verbal portion of SAT exam for those taking the exam in 2016 follow a normal distribution with a mean of 600 and a standard deviation of 125. We plan to take a simple random sample (SRS) of300 SAT takers from 2013 and record the verbal score for each person in the sample. a. What is the population of interest in this problem? b. What variable is recorded on each unit in the population? c. What type of variable is being recorded? (Categorical or Quantitative?) d. What are the parameters of interest in the problem? (Include the correct symbol). a. Once a sample is selected, the mean of the 300 scores in the sample will be determined. Is this quantity a parameter or a statistic? Explain for full credit. b. What is the sampling distribution of the sample mean for samples of size 300. Verify that the condition hold for the CLT for sample means. Suppose you want the standard deviation of the sample mean to be 10 or less. How large of a sample needs to be selected? Show your work. Round up to the next whole number.

Explanation / Answer

Q1

a) SAT takers

b) Score of verbal portion of SAT exam

c) quantitative

d) mean and variance

Q2

a) statistic: A statistic is any number calculated from a sample.

b) The sampling distribution of sample mean is Normal, because sample size is large enough

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