A statistician selected a random sample of 125 observations from a population with a known standard deviation equal to 16 and computed a sample mean equal to 77. (SHOW WORK for CREDIT; round to 3 decimal places) a) Estimate the population mean with 93% confidence. b) Repeat Part a) using a 89% level of confidence. c) Repeat Part a) using a population variance equal to 441. d) Repeat Part a) using a sample size equal to 625. Any changes to C. I.?

Step-by-step explanation:

Given that a statistician selected a random sample of 125 observations from a population with a known standard deviation equal to 16 and computed a sample mean equal to 77

We can use Z critical values since population std deviation is known. Also sample size >30

We find std error of mean =

Margin of error = Z critical value * 1.4311

Z critical values for 93% = 1.81

for 89% = 1.60

nStd errorZ critical  Conf interval  

            89%    

1251.4311     1.6  (74.7102479.28976 )

          93%    

            1.81  (74.40970979.590291 )

We find that when confidence level increases interval width increses.

c) When sigma changes to 441, std error changes to

So we get

nStd errorZ critical  Conf interval  

           89%    

441  0.7619     1.6  (75.78178.219 )

         93%    

           1.81  (75.62178.37904)

d) When n = 625, std error changes to 16/25 = 0.64

nStd errorZ critical  Conf interval  

        89%    

4410.641.6        (75.97678.024 )

       93%    

        1.81      (75.84278.1584)

When sample size increases, confidence interval width decreases.

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form