Question

The grade point average for 7 randomly selected college students is:
2.3, 2.6, 1.2, 3.5, 2.3, 3.1, 1.3.( Assume the sample is taken from a normal distribution)
a) Find the sample mean. (show all work)
b) Find the sample standard deviation.
c) Construct a 90% C. I. for the population mean

Answer 1

Solution:

Given that,

x	x2
2.3	5.29
2.6	6.76
1.2	1.44
3.5	12.25
2.3	5.29
3.1	9.61
1.3	1.69
x =16.3	x 2  = 42.33

a ) The sample mean is

Mean   = (x / n)

= ( 2.3+2.6+1.2+3.5+2.3+3.1+1.3 / 7 )

= ( 16.3 / 7 )

= 2.3286

Mean   = 2.33

b ) The sample standard is S

S = ( x² ) - (( x)² / n ) / 1 -n )

= ( 42.33 ( (16.3 )² / 7 ) / 6

   = ( 42.33 - 37.9557 / 6 )

= (4.3743 / 6 )

= 0.729

= 0.8538

The sample standard is = 0.85

c ) = 2.33

s = 0.85

n = 7

Degrees of freedom = df = n - 1 = 7 - 1 = 6

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,6 =1.943

Margin of error = E = t_/2,df * (s /n)

= 1.943 * (0.85 / 7)

= 0.62

The 95% confidence interval estimate of the population mean is,

- E < < + E

2.33 - 0.62 < < 2.33 + 0.62

1.71 < < 2.95

(1.71, 2.95 )