Question

Eight trials are simulated. The results are shown in the table. Simulation 109 105 112 110 115 106 108 109 What is the estimated margin of error, using standard deviation? Enter your answer, rounded to two decimal places, in the box.

Answer 1

Answer:

a) The Margin of error = 2.6723

b) The Standard error  = 1.1299

Step-by-step explanation:

Given data

x          109         105     112        110        115       106      108       109

Mean of x    =    $\frac{109 +105 + 112 + 110 +115+ 106 +108+ 109}{8} = 109.25$

x⁻ = 109.25

  x  :     109   105       112      110       115       106        108         109

x- x⁻  : -0.25   -4.25   2.75    0.75    5.75     -3.25     -1.25      -0.25

(x-x⁻)²: 0.062 18.062 7.562  0.562  33.062  10.562 1.562  0.062

∑((x-x⁻)² =   71.5

$S^2 = \frac{71.5}{8-1} = \frac{71.5}{7} =10.2142$

The Standard deviation of sample S = 3.1959

a)

The Margin of error is determined by

$M.E = t_{\frac{\alpha }{2} } \frac{ S}{\sqrt{n} }$

Degrees of freedom γ =n-1 = 8-1 =7

$t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025} = 2.365$

$M.E = 2.365{ \frac{ 3.195}{\sqrt{8} }$

The Margin of error = 2.6723

b) The Standard error is determined by

$S.E = \frac{ S}{\sqrt{n} }$

$S.E = \frac{ S}{\sqrt{n} } = \frac{3.1959}{\sqrt{8} } = 1.1299$

The Standard error  = 1.1299