The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. a random sample of 12 employees reveals the following family dental expenses (in dollars): 115 370 250 593 540 225 117 425 318 182 275 228 construct a 95% confidence interval for the average family dental expenses for all employees in this corporation. place your lower limit, in dollars rounded to 1 decimal place, in the first blank. do not use a dollar sign, a comma, or any other stray mark. for example, 123.4 would be a legitimate entry. place your upper limit, in dollars rounded to 1 decimal place, in the second blank. do not use a dollar sign, a comma, or any other stray mark. for example, 567.8 would be a legitimate entry.

CI(95%): [205,5;400.8]dolars

Step-by-step explanation:

Hello!

So you need to construct a confidence interval for the average family dental expenses (μ) using the sample given in the problem. To estimate it you need to first choose a statistic. For this small sample, considering that the variable has a normal distribution (I made a quick Shapiro Wilks test, with p-value 0.3234, you can assume normality) the best statistic to use is the Student's t-test.

t= [x(bar)-μ]/S/√n ≈ t₍ₙ₋₁₎

The formula for the confidence interval to estimate the mean is

x(bar)±* (S/√n)

The critical value is from a t-distribution with 11 degrees of freedom

±

>remember since it's two-tailed, to get the right critical value you have to divide α by 2. So in the text, you received a confidence level of 1-α=0.95 so α=0.05 then α/2=0.025 and 1-α/2=0.975

To construct the interval, you need to first calculate the sample mean and the standard derivation.

Sample

115; 370; 250; 593; 540; 225; 117; 425; 318; 182; 275; 228

n= 12

∑xi = 3638 ∑xi² = 1362670

Sample mean

x(bar): (∑xi)/n = 3638/12 = 303.17 dolars

Standard derivation

S²= 1/n-1*[∑xi²- (∑xi)²/n] = 1/11 * [1362670-((3638)²/12)] = 23614.47 dolars²

S= 153.67 dolars

Confidence interval (95%)

303.17± 2.201* (153.67/√12)

[205,5;400.8]dolars

I hope you have a SUPER day!

answer: 21$

step-by-step explanation:

$42 / $14 = 3   (ratio 3: 1)

$7 x 3 = $21

the cat is blue because the probability of extension towards the prefix of the diameter of the circle could only mathematically equal to the sum of the roots of the carrots from   your garden.

step-by-step explanation: