Later , another seven metal ingots were chosen at random and measurements were made of their hardness h . The results are shown in the table below .
Hardness ( h ) 67 82 79 63 90 80 83
A t -test is conducted at a 5 % significance level to investigate whether the means of hardness �
1 and �
2 from the two samples are different .
( e ) ( i ) Write down the alternative hypothesis of the test .
( ii ) Find the p -value .
( iii ) Hence , state the conclusion of the test with a reason . [ 5 ]
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