In: Statistics and Probability
Solution:
x | x2 |
35 | 1225 |
90 | 8100 |
105 | 11025 |
45 | 2025 |
120 | 14400 |
65 | 4225 |
30 | 900 |
23 | 529 |
100 | 10000 |
110 | 12100 |
105 | 11025 |
95 | 9025 |
105 | 11025 |
60 | 3600 |
110 | 12100 |
120 | 14400 |
95 | 9025 |
90 | 8100 |
60 | 3600 |
70 | 4900 |
x=1633 | x2=151329 |
The sample mean is
Mean
= (x
/ n) )
=35+90+105+45+120+65+30+23+100+110+105+95+105+60+110+120+95+90+60+7020
=163320
=81.65
Mean = 81.65
The sample standard is S
S =(
x2 ) - ((
x)2 / n ) n -
=√(151329-(1633)220) 19
=√(151329-133334.45) 19
=√17994.55 /19
=√947.0816
=30.7747
sample Standard deviation S= 30.77
n = 20
Degrees of freedom = df = n - 1 = 20 - 1 = 19
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
t /2,df = t0.05,19 =1.729
Margin of error = E = t/2,df * (s /n)
= 1.729* (30.77 / 20)
= 11.90
Margin of error = 11.90
The 90% confidence interval estimate of the population mean is,
- E < < + E
81.65 - 11.90 < < 81.65 + 11.90
69.75 < < 93.55
lower limit= 69.75
upper limit= 93.55