Statistics is kicking my butt,Can you help?
I would really appreciate an explanation!
A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. The scores are normally distributed. Construct a 95% confidence interval for the standard deviation of the scores of all subjects taking this test. Round the confidence interval limits to 2 decimal places.
n=____
s=____
z(2/l)=____
z(2.r)=____
INTERVAL:
2.The daily intakes of milk (in ounces) for ten randomly selected people are given below. Construct a 95% confidence interval for the population standard deviation. The values are normally distributed. Round the confidence interval limits to 2 decimal places.
22.312.923.126.310.8
26.827.429.719.019.9
n=____
s=____
z(2/l)=____
z(2.r)=____
INTERVAL:
1)
n=27
s=21.4
z(2/l)=13.844
z(2/r)=41.983
Standard deviation = 21.4
Chi squared = (n-1)s^2 / σ^2
Chi squared degree of freedom = 26
Confidence limits 26(21.4)(21.4)/(41.983)
and 26(21.4)(21.4)/(13.844)
95 % Confidence interval for σ^2
(283.6138 , 860.0809)
Confidence limits for σ
(16.8408 , 29.3271)
2)
Number of cases 10
To find the mean, add all of the observations and divide by 10
Mean 21.82
Squared deviations
(22.3-21.82)^2 = (0.48)^2 = 0.2304
(12.9-21.82)^2 = (-8.92)^2 = 79.5664
(23.1-21.82)^2 = (1.28)^2 = 1.6384
(26.3-21.82)^2 = (4.48)^2 = 20.0704
(10.8-21.82)^2 = (-11.02)^2 = 121.4404
(26.8-21.82)^2 = (4.98)^2 = 24.8004
(27.4-21.82)^2 = (5.58)^2 = 31.1364
(29.7-21.82)^2 = (7.88)^2 = 62.0944
(19-21.82)^2 = (-2.82)^2 = 7.9524
(19.9-21.82)^2 = (-1.92)^2 = 3.6864
n=10
s=3.6864
z(2/l)=2.7
x(2/r)=19.023
Variance (using n-1) = 352.616/9
Variance 39.1796
Standard deviation (using n-1) = sqrt(variance) = 6.2594
Chi squared = (n-1)s^2 / σ^2
9 degrees of freedom
Confidence limits 9(6.2594)(6.2594)/(19.023)
and 9(6.2594)(6.2594)/(2.7)
Confidence limits for σ^2
(18.5366 , 130.6003)
Confidence limits for σ
(4.3054 , 11.428)
All Aboard! Public Transit Ridership Reaches Highest Level i
