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

Question

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. Use the two-sample t test at significance level 0.01 to test H0: 1 2 = 10 versus Ha: 1 2 < 10 for the following data: m = 5, x = 115.2, s1 = 5.05, n = 5, y = 129.3, and s2 = 5.31.

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

State the conclusion in the problem context.

Reject H0. The data suggests that the difference between mean stopping distances is less than 10.

Reject H0. The data does not suggest that the difference between mean stopping distances is less than 10.    

Fail to reject H0. The data suggests that the difference between mean stopping distances is less than 10.

Fail to reject H0. The data does not suggest that the difference between mean stopping distances is less than 10.

Explanation / Answer

Compute 2-sample t test statistic:

SE(xbar-ybar)=sqrt[s1^2/m+s2^2/n]

=sqrt[5.05^2/5+5.31^2/5]

=3.277

t=(xbar-ybar)-0/SE(xbar-ybar)=(115.20-129.30)-0/3.277

=-4.30

At df=7, the p value is 0.004.

The p value is less than alpha=0.01. Reject HO.

Option 1)

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