Question

Do adult learners and traditional students differ in terms of how many hours per week they plan to devote to PSY 298 on average?

Data were taken from a sample of students. A hypothesis test was conducted and the null hypothesis was not rejected. In other words, the result was to fail to reject the null hypothesis.

Later, data from the entire population were available. Using that population data, the researchers found that there was a difference in how many hours per week adult learners and traditional students planned to devote to PSY 298.

Was a Type I or Type II error committed here?

And could you explain WHY? OR please explain the difference between a Type I or Type II error in easily

Answer 1

A Type I error is the probability of rejecting the null hypothesis when it is true

while

A Type II error is the probability of not rejecting the null hypothesis even when it is not true

Let be the population mean number of hours the adults and the students devote to PSY298 respectively

The null hypothesis always contains the equal to condition

Thus, the null and alternative hypotheses are

The null hypothesis was not rejected that is; a conclusion was made that the means are equal

But when the population study was conducted the means were found to be different. Which implies that the null hypothesis was not true.

Thus the null hypothesis was not rejected although it was not true

Hence, a Type II error was committed

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