An aspirin manufacturer fills bottles by weight rather than by count. The weight

Question

An aspirin manufacturer fills bottles by weight rather than by count. The weight per tablet should be 5 grains. Each of 100 tablets taken from a very large lot is weighted resulting in a sample average weight per tablet of xbar= 4.89 grains and a sample standard deviation of s = 0.26 grain.

When testing the hypotheses H0: = 5 against the alternative hypothesis HA: 5, a type-II-error would be
concluding that the tablets weigh 5 grains, when in fact they do not
concluding that the tablets do not weigh 5 grains, when in fact they do
there is no error as long as the pvalue is less than
concluding that the tablets weigh 4.89 grains, when in fact they weigh 5 grains

When testing the hypotheses H0: = 5 against the alternative hypothesis HA: 5, a type-I-error would be
concluding that the tablets weigh 4.89 grains, when in fact they weigh 5 grains
there is no error as long as the pvalue is less than
concluding that the tablets do not weigh 5 grains, when in fact they do
concluding that the tablets weigh 5 grains, when in fact they do not

Explanation / Answer

A type II error is the failure to reject a false null hypothesis (a "false negative"). Thus here type II error will be concluding that the tablets weigh 5 grains, when in fact they do not .

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive").

a type-I-error would be
concluding that the tablets do not weigh 5 grains, when in fact they do

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