Question

20 students were surveyed and had an average GPA of 2.6 with a standard deviation of 0.3.

(a) Calculate the margin of error for a 95% confidence level.

(b) Find a 95% confidence interval on the average GPA. Provide a practical interpretation of this interval.

Answer 1

using T score as sample size is small and unknown population standard deviation.

x?= 2.6

s= 0.3

n= 20

Df=20-1=19

alpha=0.05 then T(alpha/2)=2.093024054

Margin of error E= T(alpha/2)*s/sqrt(n)

=2.093*0.3/sqrt(20)

=0.14040................Answer for A

95% Confindence interval for population mean =(x?-E,x?+E)

rounded upper bound= 2.7404

rounded lower bound= 2.4596

..........Answer for B

we are 95% confident that true population mean of GPA fall between 2.4596 and 2.7404.

if you have any doubt ask in comment , give thumbs up if you like work.