The standard deviations s for the annual medical costs 30 heart disease patients was found to equal $1005. Find a 95 % confidence interval for the standard deviation of the annual medical costs for all heart disease patients.
N=30
http://www.milefoot.com/math/stat/ci-variances.htm
One hundred subjects in a psychological study had a mean of 35 on a test instrument designed to measure anger. The study the ó=10. Find a 99% confidence interval for the mean anger score of the population.
95% = mean ± 1.96 SEm
99% = mean ± 2.575 SEm
SEm = SD/√n
what is n
To find the 95% confidence interval for the standard deviation of the annual medical costs for all heart disease patients, we can use the Chi-Square distribution.
The Chi-Square distribution is commonly used to estimate the confidence interval for the population standard deviation when the sample standard deviation is known.
The formula to calculate the confidence interval for the standard deviation (σ) is:
CI = [(n - 1) * s² / X²₀₅, (n - 1) * s² / X²₀.₀₅]
Where:
- CI is the confidence interval
- n is the sample size (number of heart disease patients in this case)
- s is the sample standard deviation (given as $1005 in this case)
- X²₀₅ and X²₀.₀₅ represents the critical values from the Chi-Square distribution table for the desired level of significance (95% confidence level in this case). The subscript ₀.₀₅ represents the upper tail critical value, and the subscript ₀₅ represents the lower tail critical value.
We need the critical values from the Chi-Square distribution table. For a 95% confidence level, the upper tail critical value is 0.05, and the lower tail critical value is also 0.05. From the table, these values correspond to the degrees of freedom (df) of n - 1.
Once you find the critical values, plug them and the given values into the formula to calculate the confidence interval.
Note: The degrees of freedom (df) is equal to n - 1 because we need to subtract 1 from the sample size to estimate the population parameter.
I don't have the exact sample size (n) from your question. If you provide the value, I can help you calculate the confidence interval.