Question

The data below give the weights in ounces of randomly-selected bars of bath soap produced by two different molding machines.

	Weights
Machine 1	11.4	12.4	12.1	11.8	11.8	11.7	12.3	12.0	11.8
Machine 2	13.0	12.4	12.4	12.1	12.3	12.1	12.5	12.0	12.1

The question of interest is whether these two molding machines produce soap bars of differing average weight. Find the P-value for the this test assuming that the weights for the two machines are approximately normal..

Group of answer choices

0.014

0.038

0.054

0.311

Answer 1

	Machine 1	Machine 2
mean	11.922	12.322
std. dev.	0.311	0.307
n	9	9

To Test :-

H0 :- µ1 = µ2
H1 :- µ1 ≠ µ2

Test Statistic :-
t = (X̅1 - X̅2) / SP √ ( ( 1 / n1) + (1 / n2))
$S_{p} = ( \sqrt{( n1 - 1 )S_{1}^{2} + (n2 - 1 )S_{2}^{2} ) / ( n1 + n2 - 2 )}$

Sp = 0.3093

t = - 2.74

P value = 2 * P ( t > 2.44 ) = 0.0144

Correct option is 0.014