Introduction of confidence interval standard deviation:
When a point estimate is used to estimate the parameter of interest, it is unlikely that the value of the point estimate is equal to the value of the parameter. Therefore, we will use the value of the point estimation to help construct an interval estimate for the parameter, we will be able to state, with some confidence, that the parameter lies with in the interval,and because of this we refer to these intervals as confidence intervals. Typically, we consider, 95 percent, and 99 percent interval estimates for the parameters. but, any other percentage can be considered.
Examples of Confidence Interval Standard Deviation :
A Random sample of 100 school teachers in a particular state has a mean salary of $31,578. It is knwon from the previous data that the standard deviation of the salaries of the teachers in the state is $4,415. Construct a 99% confidence interval estimate for the true mean salary for public school teachers for a given state. Having problem with how to divide radicals keep reading my upcoming posts, i will try to help you.
Solution: Given α = 0.01, Zα/2 = 2.576, x¨= 31578, n=100 , σ = 4,415 and σx = σ / √n = 441.5
Thus the 99 percent confidence interval estimate for the mean salary, using the formula, is 31,578 ± 2.576 x 441.5 = 31,578 ± 1,137.3. That is we are 99 percent confident that the average salary of the public school teachers for the given state will be between $30,440.9 and $32,715.3.
When a point estimate is used to estimate the parameter of interest, it is unlikely that the value of the point estimate is equal to the value of the parameter. Therefore, we will use the value of the point estimation to help construct an interval estimate for the parameter, we will be able to state, with some confidence, that the parameter lies with in the interval,and because of this we refer to these intervals as confidence intervals. Typically, we consider, 95 percent, and 99 percent interval estimates for the parameters. but, any other percentage can be considered.
Examples of Confidence Interval Standard Deviation :
A Random sample of 100 school teachers in a particular state has a mean salary of $31,578. It is knwon from the previous data that the standard deviation of the salaries of the teachers in the state is $4,415. Construct a 99% confidence interval estimate for the true mean salary for public school teachers for a given state. Having problem with how to divide radicals keep reading my upcoming posts, i will try to help you.
Solution: Given α = 0.01, Zα/2 = 2.576, x¨= 31578, n=100 , σ = 4,415 and σx = σ / √n = 441.5
Thus the 99 percent confidence interval estimate for the mean salary, using the formula, is 31,578 ± 2.576 x 441.5 = 31,578 ± 1,137.3. That is we are 99 percent confident that the average salary of the public school teachers for the given state will be between $30,440.9 and $32,715.3.
No comments:
Post a Comment