The grade point averages (GPA) for 12 randomly selected college students are shown on the right. Complete parts (a) through (c) below. Assume the population is normally distributed. 2.2 3.2 2.5 1.6 0.6 4.0 2.3 1.3 3.6 0.3 2.3 3.4
a) Find the sample mean.
x overbar x equals=
(Round to two decimal places as needed.)
(b) Find the sample standard deviation.
s equals=
(Round to two decimal places as needed.)
(c) Construct a
95%
confidence interval for the population mean
muμ.
A
95%
confidence interval for the population mean is left parenthesis nothing comma nothing right parenthesis .,.
(Round to two decimal places as needed.)
Solution :
Using calculator,
(a)
= 27.3 / 12 = 2.28
(b)
s = 1.17
(c)
t_{ /2,df} = 2.201
Margin of error = E = t_{/2,df} * (s /n)
= 2.201 * (1.17 / 12)
Margin of error = E = 0.74
The 95% confidence interval estimate of the population mean is,
- E < < + E
2.28 - 0.74 < < 2.28 + 0.74
1.54 < < 3.02
(1.54 , 3.02)
The grade point averages (GPA) for 12 randomly selected college students are shown on the right....
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