1. (4 points) One scale used to measure depression is the Hamilton rating scale.

Question

1. (4 points) One scale used to measure depression is the Hamilton rating scale. Scores of - 7 are considered to be normal. Scores are skewed right, with a known population standard deviation of 3.2. Suppose a simple random sample of 35 undergraduates is taken and their mean score is 4.9. You can assume the population standard deviation for the undergraduates is the same as the general population. You want to build a confidence interval to estimate the true mean score for all undergraduates. Should you use a T-distribution or a Z-distribution? Tdistibution a. b. What is the point estimate for the undergraduate population average score? 3 c. Calculate the 90% confidence interval.

Explanation / Answer

a) as population std deviation known we should use zdistribution

b) point estimate =4.9

c)

for std errror of mean =std deviation/(n)1/2 =3.2/(35)1/2 =0.5409

for 90% confidence interval ; crtiical value of z =1.6445

therefore 90% confidence interval =sample mean -/+ z*std error =4.0103 ; 5.7897

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