The Central Limit Theorem Preview CT-STEM

Difference between Two Sample Means

From our formula sheet:

ACT scores at Ardrey Kell High School are Normally distributed with mean 26 and standard deviation 3. ACT scores at Providence HS are skewed to the right with mean 25 and standard deviation 5.

Questions

Please answer the questions below.

Question 6.1

We randomly select 25 students from AKHS and 30 students from PHS. Use the information given to describe the sampling distributions of the average ACT scores for the two samples.

Question 6.2

Suppose we took a sample of 25 students from AKHS and a sample of 30 students from PHS and found the difference in the sample means. Describe the sampling distribution of the difference in mean ACT scores (AKHS – PHS). Be sure to address shape, mean and standard deviation.

Question 6.3

Calculate the probability that random sample of 25 AKHS students has a higher mean ACT score than the random sample of 30 PHS students. Upload scanned image of work.

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Notes

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