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# Six Sigma Tools for Testing Statistical Significance

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"Suppose you want to know if a new design of a product is actually better than the current product. For example, your design team is working on increasing the speed of the KX Speed Drill. You have produced a small batch of the new design, the KX2, and you want to know if this speed is faster than the current speed of 17.5 revs per second.

To test the new design, QA has taken a sample of 13 KX2's and clocked their speed. The results of this test are shown below.

Is it safe to conclude that the new design for the KX2 has a significantly higher speed with a confidence of 1%?"

DATA

1 --18.4
2 --19.3
3 --20.5
4 --18.6
5 --17.8
6 --21.0
7-- 19.4
8 --19.2
9 --18.9
10 --15.9
11 --17.7
12 --20.5
13 --19.1

https://brainmass.com/statistics/hypothesis-testing/six-sigma-tools-for-testing-statistical-significance-545583

#### Solution Preview

For the given sample data,
Mean, Xbar = 18.95 [see excel file for this estimation.]
Standard deviation, s = 1.36 [see excel file for this estimation.]
No. of data in the sample, n = 13

For the population,
mean, mu = 17.5

Null ...

#### Solution Summary

A problem is solved to statistically test if the new design of a Speed Drill has improved speed.

\$2.19
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## Six Sigma Tools for Testing Statistical Significance in Sleep

Sam Sleep researcher hypothesizes that people who are allowed to sleep for only four hours will score significantly lower than people who are allowed to sleep for eight hours on a management ability test. He brings sixteen participants into his sleep lab and randomly assigns them to one of two groups. In one group he has participants sleep for eight hours and in the other group he has them sleep for four. The next morning he administers the SMAT (Sam's Management Ability Test) to all participants. (Scores on the SMAT range from 1-9 with high scores representing better performance). Is Sam's hypothesis supported by this data? perform a t-test.

SMAT scores

8 hours sleep group (X)
5
7
5
3
5
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9

4 hours sleep group (Y)
8
1
4
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1
2

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