1. The modulus of tungsten alloy armor plate is typically 147 GPa, with a standard deviation of < 10 GPa. Your company is a large supplier of this armor plate to the manufacturers of M1 Abrams tank industry. Your competitor recently announced that his armor plate has a modulus of at least 167 GPa, with a standard deviation of <7 GPa. This claimed greater modulus and "tighter" sigma will enable armor plate that is 20% lighter than those made from your plate. So, you are anxious to evaluate the claim. You obtain twenty samples of this plate and measure the following moduli. (Note if there are any questionable data points. Discuss the normality of the data, but analyze as if the data were normal. These data were generated with a normal random number generator):

167.7

149.3

160.2

165.4

165.0

167.5

158.1

167.5

164.5

163.6

165.5

160.5

165.5

164.1

165.1

168.4

166.2

167.0

169.7

167.2

Set up and perform a hypothesis test to evaluate the competitor's claim for the mean. Use 95% confidence.

- I believe it's 164.4 plus/minus 2.0 (162.4, 166.4) - Can you just confirm?

Sample mean = 164.4

StdDev = 4.6

Set up and perform a hypothesis test or a confidence interval to evaluate the competitor's claim for the standard deviation. Use 95% confidence.

- I believe this is the answer - Can you just confirm?

H0 mean = 167 (no difference between the means of the companies' armor plates)

H1 mean < 167 (significant difference between the means of the companies' armor plates)

T0= (164.4-167) / (4.6/ sqrt 20) = -2.61

t= t (0.05),19= -1.73

-2.61 < -1.73

Reject null hypothesis; competitors claim is not acceptable at 95% confidence

1. - In a large population, what % of the samples would you expect to be below 160 GPa
2. - What chance is there for a Type II Error, if the mean should be >162.
3. - Discuss the results and what you would do with the data.