For a sample of nine automobiles, the mileage (in 1000s of miles) at which the o

Question

For a sample of nine automobiles, the mileage (in 1000s of miles) at which the original front brake pads were worn to 10% of their original thickness was measured, as was the mileage at which the original rear brake pads were wom to 10% of their original thickness. The results are given in the following table Front 32.8 26.6 35.6 36.4 29.2 40.9 40.9 34.8 36.6 Rear 39.8 35.2 46.1 46 39.9 51.7 51.6 46.1 47.3 Automobile 2 4 7 Let Hx represent the population mean for rear brake pads and let y represent the population mean for front brake pads. Find a 95% confidence interval for the difference ?D=??_??. Round the answers to three decimal places The 95% confidence interval for the difference in mean is 11.047 , -8.930 ).

Explanation / Answer

Sol:use R software:

FRONT <- c(32.8,26.6,35.6,36.4,29.2,40.9,40.9,34.8,36.6)
REAR <- c(39.8,35.2,46.1,46,39.9,51.7,51.6,46.1,47.3)
t.test(REAR,FRONT)

output:

Welch Two Sample t-test

data: REAR and FRONT
t = 4.0899, df = 15.667, p-value = 0.0008891
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
4.80239 15.17539
sample estimates:
mean of x mean of y
44.85556 34.86667

ANSWER:

95 percent confidence interval forr diff in means
4.802, 15.175

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