Question

# The grade point averages​ (GPA) for 12 randomly selected college students are shown on the right....

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.

2.3 3.4 2.8 1.8 0.9 4.0 2.5 1.1 3.8 0.5 2.2 3.2

​(a) Find the sample mean. x overbarequals =

​(Round to two decimal places as​ needed.)

​(b) Find the sample standard deviation. sequals =

(Round to two decimal places as​ needed.)

​(c) Construct a 95​% confidence interval for the population mean mu.

A 95​% confidence interval for the population mean is left parenthesis = comma right parenthesis .=

​(Round to two decimal places as​ needed.)

the necessary calculation table is :-

 GPA(x) x2 2.3 5.29 3.4 11.56 2.8 7.84 1.8 3.24 0.9 0.81 4 16 2.5 6.25 1.1 1.21 3.8 14.44 0.5 0.25 2.2 4.84 3.2 10.24 sum=28.5 sum=81.97

sample size(n) = 12

a).the sample mean is:-

b). the sample standard deviation is:-

c).degrees of freedom =(n-1)=(12-1)=11

t critical value for df=11,alpha=0.05, both tailed test be:-

[ using t distribution table ]

A 95​% confidence interval for the population mean is:-

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