Question

An agency conducted a car crash test of booster seats for cars. The results of the tests are given, with the units being hic (standard head injury condition units). Calculate and interpret 95% confidence interval for the true mean measurement. You can assume its a normal population of measurements. Please show work. 774 649 1210 546 431 612

Answer 1

ANSWER:

Given that,

An agency conducted a car crash test of booster seats for cars. The results of the tests are given, with the units being hic (standard head injury condition units). Calculate and interpret 95% confidence interval for the true mean measurement. You can assume its a normal population of measurements. Please show work.

774 649 1210 546 431 612

=x / n = (774+649 +1210+ 546+ 431+ 612)/6

= 4222/6

= 703.667

s = sqrt((x-)^2 / (n-1))

= sqrt((774-703.667)^2+(649-703.667)^2 +(1210-703.667)^2+ (546-703.667)^2+ (431-703.667)^2+ (612-703.667)^2)/(6-1))

= 121.97005

95% confidence interval:

c = 95% = 95/100 = 0.95

= 1-c = 1-0.95 = 0.05

/2 = 0.05/2 = 0.025

Degree of freedom = df = n-1 = 6-1 = 5

Critical value = t/2,df = t0.025,5 = 2.570543

95% CI = t/2,df * (s/sqrt(n))

95% CI = 703.667   2.570543 * (121.97005/sqrt(6))

95% CI = 703.667   127.9977836

95% CI = ( 703.667- 127.9977836 , 703.667 +127.9977836 )

95% CI = ( 575.6692164 , 831.6647836 )

95% CI = ( 575.6692 , 831.6648) (Rounded to four decimal places)

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