Question

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.)

Answer 1

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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