# A random sample of 50 recent college graduates results in a mean time to graduate of (_ over X)=4.58 years, with a standard deviation, s=1.10 years.a. Compute and interpret a 90% confidence...

A random sample of 50 recent college graduates results in a mean time to graduate of (_ over X)=4.58 years, with a standard deviation, s=1.10 years.

a. Compute and interpret a 90% confidence interval for time to graduate with a bachelor's degree.

b. Does this evidence contradict the widely held belief that it takes 4 years to complete a bachelor's degree? Why?

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Given `bar(x)=4.58,s=1.10,n=50`

The population mean `mu` lies in the interval:

`bar(x)-t_(alpha/2)(s/sqrt(n))<=mu<=bar(x)+t_(alpha/2)(s/sqrt(n))`

where alpha comes from the confidence level, and we use the student's t-table since we only have the sample standard deviation.

For a 90% confidence level `alpha=.1,alpha-2=.05` . The degrees of freedom are 49. If you use a t-table, you might find that for d.f.>29 you would use 1.645. From a calculator, I found 1.67.

`4.58-1.67(1.1/sqrt(50))<=mu<=4.58+1.67(1.1/sqrt(50))`

`4.32<=mu<=4.84`

Thus with 90% confidence we can claim that the population mean lkies in the interval `4.32<=mu<=4.84` .

(b) With 90% certainty we can claim that it takes longer than 4 years to get a bachelors degree.