A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data for a particular clinic follows (the reported variable is the number of CAT scans each month expressed as the number of CAT scans per thousand members of the health plan): 2.31, 2.09, 2.36, 1.95, 1.98, 2.25, 2.16, 2.07, 1.88, 1.94, 1.97,2.02. (a) Find a two-sided 95% confidence interval for the standarddeviation.(b) What should you do to address any reservations about theconfidence interval you found in part (a)?

a) σ_95% = [ ± 0.09934 ]

b) Increase the number of samples taken from each clinic and find their average over course of months for the entire year.

Step-by-step explanation:

Solution:-

- The data from the health provider for the number of CAT scans performed in a month in its clinics.

- The reported variable "X" : number of CAT scans each month expressed as the number of CAT scans per thousand members of the health plan.

- The statistical results were obtained as follows:

           2.31, 2.09, 2.36, 1.95, 1.98, 2.25, 2.16, 2.07, 1.88, 1.94, 1.97,2.02

- We see that a samples were taken from n = 12 clinics were taken. The sample mean ( x_bar ) can be calculated from the following descriptive stats formula:

- Similarly, we will compute the sample standard deviation ( s ) ( Normally distributed population ) for unknown population standard deviation ( σ ), the following formula is used:

- We have two parameters ( x_bar and s ) for the approximated normal distribution of random variable X with unknown population:

                       x_bar = 2.0817

                       s = 0.15636

- The sample size n = 12 ≤ 30 and unknown population standard deviation standard normal distribution is not applicable. In such case we use t-distributions for test statistics and rejection criteria.

                       degree of freedom = n - 1 = 12 - 1 = 11

                       CI (two sided ) = 95%

                       Significance Level (α) = 1 - CI = 1-0.95 = 0.05

- To determine the t-critical value defined by the significance level of two sided test we have:

                      t-critical = t_α/2 = t _ 0.025

                      t-critical =  t _ 0.025 = ±2.201

- We will now construct a 95% confidence interval for the population standard deviation ( σ ).

                      σ_95% = [ -t-critical * ( s / √n ) , t-critical * ( s / √n ) ]

                      σ_95% = [ -2.201 * ( 0.15636 / √12 ) , 2.201 * ( 0.15636 / √12 ) ]  

                      σ_95% = [ ± 0.09934 ]                      

- To address any reservation to the standard error in standard deviation can be curtailed by increasing the sample size ( n ) at-least enough for the distribution "X" to assume standard normality. n ≥ 30

this is a very good question

step-by-step explanation:

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introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.