A statistics professor at a large state university is interested in estimating t

Question

A statistics professor at a large state university is interested in estimating the mean time it takes students enrolled in an elementary statistics class to solve a problem. Since her class is very large, she decides to take a sample of size 12 to estimate the population mean (that is, the mean for the entire class). She randomly selects 12 students, gives them the exact same problem, and they work on the problem under identical conditions. The times (in minutes) for the students to solve the problem can be found below.

a.) What is the point estimate of the mean amount of time to do the problem? What is the biggest flaw of using a point estimate?

b.) Construct the 95% confidence interval for the population mean.

c.) Interpret this result.

Time (Minutes)
13.15
15.05
13.62
16.64
17.04
16.66
14.39
24.04
17.87
17.21
15.10
14.41

Explanation / Answer

(a) point estimate is sample mean=sum/n=195.18/12=16.27

point estimate may not be representative of the population

(b)

(1-alpha)*100% confidence interval for population mean=sample mean±t(alpha/2,n-1)*sd/sqrt(n)

95% confidence interval for population mean=mean±t(0.05/2, n-1)*sd/sqrt(n)=16.27±2.2*2.88/sqrt(12)=

=16.27±1.83=(14.44, 18.10)

(c)

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