Suppose 1 and 2 are true mean stopping d stances at 50 mph for cars of a certain

Question

Suppose 1 and 2 are true mean stopping d stances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m 8 115 s1 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2, (Round your answers to two decimal places.) SOS n 8, 129.8, and s2 5.33. Calculate a Does the interval suggest that precise information about the value of this difference is available? Because the interval is so wide, it appears that precise information is not available. O Because the interval is so narrow, it appears that precise information is not availeble Because the interval is so wide, it appears that precise information is available. Because the interval is so narrow, it appears that precise information is available. You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Resd Talk to a Tutor

Explanation / Answer

CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )

Where,

x1 = Mean of Sample 1, x2 = Mean of sample2

sd1 = SD of Sample 1, sd2 = SD of sample2

a = 1 - (Confidence Level/100)

ta/2 = t-table value

CI = Confidence Interval

Mean(x1)=115.5

Standard deviation( sd1 )=5.05

Sample Size(n1)=8

Mean(x2)=129.8

Standard deviation( sd2 )=5.33

Sample Size(n2)=8

CI = [ ( 115.5-129.8) ±t a/2 * Sqrt( 5.05)^2/8+(5.33)^2/8)]

= [ (-14.3) ± t a/2 * (2.595) ]

= [ (-14.3) ± 2.365 * (2.595) ]

= [-20.43717, -8.16285]

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