See Section 9.2.) Suppose 1 and 2 are true mean stopping distances at 50 mph for
ID: 3310517 • Letter: S
Question
See Section 9.2.) Suppose 1 and 2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m 5 1 43 si 5 s, n 5 y = 129.6, and s2-5.33. Calculate a 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. Does the interval suggest that precise information about the value of this difference is available? o Because the interval is so wide, it appears that precise information is not available. Because the interval is so narrow, it appears that precise information is not available. 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 apprope table in the Appendix of Tables (Table A.5) to answer this question.Explanation / Answer
Solution:- Given The data follows: m = 5, x = 114.3, s1 = 5.05,
n = 5, y = 129.6 and s2 = 5.33.
=> pooled standard deviation is, df = 5+5-2 = 8
Sp = sqrt[((m-1)s1^2 + (n-1)s2^2)/(m+n-2)]
= sqrt[((4 * 5.05^2) + (4 * 5.33^2))/8]
= 5.1919
=>The 95% confidence interval for the difference between true average stoppin distance. t = 2.306
=> (x - y) +/- t * Sp*sqrt[(1/m)+(1/n)]
= (114.3 - 129.6) +/- 2.306*5.1919*sqrt[(1/5)+(1/5)]
= ( -22.87 , -7.73)
=> option A. Because the interval is so wide, it appears that precise information is not available.