A random sample of size n = 100 produced the sample mean of y bar = 16. Previous

Question

A random sample of size n = 100 produced the sample mean of y bar = 16. Previous studies revealed that the population standard deviation is sigma_y = 3. (a) What is the sampling distribution of the sample mean y bar? (b) Compute (approximate) 95% confidence interval for the population mean mu_y. (c) Discuss whether it is possible for the true population mean to be actually mu_y = 17? (d) The true population mean is unknown. Explain how can you improve your sample to make sure that the margin of error of estimation does not exceed 1.0?

Explanation / Answer

a) sampling distribution is approximately normal as sample size is more then 30

b) for std error =std deviation/(n)1/2 =0.3

for 95% CI, z=1.96

hence confidenc interval =sample mean -/+ z*std error =15.412 ; 16.588

c)as 17 falls outside of our 95% confidence interval; possibility of that is rare.

d)by increasing sample size , we can reduce margin of error . AS we increase sample size , the sample mean will tend to be closer to population mean

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