The factors that influence the breaking strength of a synthetic fiber are being

Question

The factors that influence the breaking strength of a synthetic fiber are being studied. Several variables were considered and preliminary data suggest that the two primary sources of variation are individual differences in machines and in operators. Four production machines and three operators are chosen and an experiment is run using fiber from the same production batch. Complete the following questions regarding this experiment:

Type ["One"/ "Two"/ "Three"/ "None of these"] error represents a 'false negative' - when we fail to reject the null hypothesis when it was actually false.

if the p-value is less than the alpha value, then we have sufficient evidence to ["Reject"/"Accept"/ "Fail to Reject"/ "Fail to Accept"] the ["Null"/"Alternative"] hypothesis.

If the test statistic falls within the rejection region, then we have sufficient evidence to ["Reject"/ "Accept"/"Fail to Reject"/"Fail to Accept"] the ["Null"/ "Alternative"]         hypothesis.

Type ["One"/"Two"/"Three"/"None of these"] error represents a 'false positive' - when the null hypothesis is rejected although it is actually true.

Explanation / Answer

Type "Two"  error represents a 'false negative' - when we fail to reject the null hypothesis when it was actually false.

If the p-value is less than the alpha value, then we have sufficient evidence to "Reject" the "Null" hypothesis.

If the test statistic falls within the rejection region, then we have sufficient evidence to "Reject" to the "Null" hypothesis.

Type "One" error represents a 'false positive' - when the null hypothesis is rejected although it is actually true.

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