Question
In: Math
Determine the 95% confidence interval for the following scores: 83, 92, 81, 87, 79, 93, 88,...
Determine the 95% confidence interval for the following scores: 83, 92, 81, 87, 79, 93, 88, 87, 83. Hint: You will need to determine the sample mean and standard deviation and then construct your confidence interval around these.
Solutions
Expert Solution
Solution:
Given that,
| x | dx=x-A = x = 86 | dx2 |
| 83 | -3 | 9 |
| 92 | 6 | 36 |
| 81 | -5 | 25 |
| 87 | 1 | 1 |
| 79 | -7 | 49 |
| 93 | 7 | 49 |
| 88 | 2 | 4 |
| 87 | 1 | 1 |
| 83 | -3 | 9 |
 x
=773 |
dx
= -1 |
dx2
= 183 |
Mean 
= x
/n
=(83+92+81+ 87+ 79+ 93+ 88+ 87+ 83 / 8 )
= 733 / 9
= 85.8889
Mean = 86
Sample standard deviation is S
=
dx2 - (( dx )2 / n) n -1 )
=
=
=
=
= 4.7813
Sample standard deviation is S = 5
= 86
s = 5
n = 8
Degrees of freedom = df = n - 1 = 8 - 1 = 7
a ) At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 =
0.025
t /2,df =
t0.025,7 = 2.365
Margin of error = E = t/2,df * (s /
= 2.365 * (5
= 4.18
The 95% confidence interval estimate of the population mean is,
- E < 
< + E
86- 4.18< < 86+ 4.18
81.82 < < 90.18
(81.82 , 90.18 )
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What are the Hypothesis Statement?
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