Question

describe a real-world example of when a hypothesis test could be used and also include a numerical example. The example can use real data or data that you make up such as values for the mean, standard deviation, and sample size.

Answer 1

An engineer measured the Brinell hardness of 25 pieces of ductile iron that were subcritically annealed. The resulting data were:

170 167 174 179 179 187 179 183 179

156 163 156 187 156 167 156 174 170

183 179 174 179 170 159 187

The engineer hypothesized that the mean Brinell hardness of all such ductile iron pieces is greater than 170. Therefore, he was interested in testing the hypotheses:

Xbar -Mean - 172.52

s - Standard deviation - 10.31

Sample size-25

H0 - mu = 170

Ha - mu > 170

T stat = ( xbar - mu ) / ( s ÷ √n ) = (172.52-170)/(10.31÷√25)

t stat = 1.22

Pvalue = P(t > 1.22) = 0.117 > 0.05 = alpha

There is insufficient evidence, at the alpha = 0.05 level, to conclude that the mean Brinell hardness of all such ductile iron pieces is greater than 170.