Question

Assume the one can of black beans weights on average 355 grams and one can of pinto beans weights on average 354 grams and both have a standard deviation of 1 gram. If you select at random 36 cans of black beans and 48 cans of pinto beans, what is the probability that the average weight of black bean cans is greater than the average weight of pinto bean cans?

Answer 1

The t statistic is used to calculate the P-value which is the the probability of the occurrence of a given event

From the data values,

	mean,	std dev,	n
black beans	355	1	36
pinto beans	354	1	48

The t statistic for the difference in means of two sample assuming equal variances is obtained using the formula,

Now, the P-value is obtained using the t distribution table for degree of freedom = n1+n2-2=36+48-2=82

The probability that the average weight of black bean cans is greater than the average weight of pinto bean cans = 0.0000108