PLEASE ANSWER THE COMPLETE QUESTION. DO NOT SKIP ANY PARTS. ANSWER EACH PART STE

Question

PLEASE ANSWER THE COMPLETE QUESTION. DO NOT SKIP ANY PARTS. ANSWER EACH PART STEP BY STEP. EXPLAIN HOW YOU ARRIVED AT THE ANSWER

3. A random smaple of 50 recent college graduates in a mean time to graduate of 4.58 years, with a standard deviation of 1.1 years.
a. Computer and interpret a 90% confidence interval for time to graduate with a bachelor's degree.
c.There is a widely held belief it takes 4 years to complete a bachelor's degree. Based on your answer in part a do you agree?
d. Suppose you want to conduct your own study to determine the number of years it takes a college student to obtain a bachelor degree. What sample size would be needed for your estimate to be within half a year at 99% confidence level?

Explanation / Answer

3a) std error =std deviation/(n)1/2 =0.1556

for 90% CI and 49 degree of freedom t =1.6766

henec confidence interval =sample mean -/+ t*std error =4.3192 ; 4.8408

above interval provide 90% probability to contain true mean of proportion

c)No as our interval does not include 4 yeears as probable value

d)for 99% CI, z=2.5758

margin of errror E =0.5

hence sample size =(z*std deviation/E)2 =~33

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