Res/342 E-Text 10.49

An experimental bumper was designed to reduce damage in low-speed collisions. This bumper was installed on an experimental group of vans in a large fleet, precisely not on a control group. At the terminus of a trial period, accident data showed 12 localisation incidents for the experimental group and 9 repair incidents for the control group. fomite downtime (in days per repair incident) is shown below. At ?= .05, did the new bumper reduce downtime? (a) pull ahead stacked dot plots of the data (a sketch is OK). (b) give in the hypotheses. (c) State the decision ascertain and sketch it. (d) Find the test statistic. (e) engender a decision. (f ) Find the p-value and interpret it. (g) Do you think the dissimilitude is large enough to be important? Explain. (Data are from an unpublished study by Floyd G. Willoughby and Thomas W. Lauer, Oakland University.)
New bumper (12 repair incidents): 9, 2, 5, 12, 5, 4, 7, 5, 11, 3, 7, 1
comprise group (9 repair incidents): 7, 5, 7, 4, 18, 4, 8, 14, 13

Solution

a) Dot plot of the data is devoted below
[pic]

[pic]

b) The null and alternative hypothesis are
[pic] and [pic].

c) Assuming equal variance, at ? = 0.05, from Students t distribution with [pic] = 12 + 9 2 = 19 degrees of freedom, the critical value of the test is obtained as 1.729.
Thus, the decision rule is
Reject H0 if [pic] < 1.729.

The sketch of the do away withion region is devoted below.





[pic]

d) The test statistic is given by,
[pic],
where [pic].
From the given data,
[pic] = 5.92, [pic]= 8.89, [pic] = 3.42, [pic] = 4.96.
Therefore,
[pic]= 17.148
Thus,
[pic] = 1.63.

e) Since t = 1.63 > 1.729, we disregard to reject the null hypothesis.

f) The p-value of the test is given by,
P[ t < -1.63] = 0.06
The decision rule using p-value is reject the null hypothesis Ho if p-value < 0.05.
Since the p-value > 0.05, we fail to reject the null hypothesis. This is a close decision.

g) A ingest difference of approximately 3 days downtime would be considered...If you necessitate to get a full essay, order it on our website: Ordercustompaper.com



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