In a t-test, when we see a difference in the means but our test leads us...

In a t-test, when we see a difference in the means but our test leads us to accept the null hypothesis, we:

Select one: 1. claim that a significant difference exists between groups. 2. have obtained a t-value greater than our critical t-value. 3. have committed a Type 1 error. 4. conclude that the difference is a result of the sampling error.

Expert Solution

Whenver null hypothesis is accepted it indicates that significant difference doesn't exist between groups. Rejection of null hypothesis leads to that conclusion.Hence first option is wrong.

If t value is greater than critical t value then the null hypothesis is rejected.Here the null hypothesis has been accepted so t value can't be greater than critical t value.So second option is wrong too.

Type I error is error committed in rejection of the null hypothesis when it is true. However here the null hypothesis has been accepted. So there is no question of rejection of true null hypothesis. So third option is wrong too.

Ideally the two different means should be equal. However some differences are there which occurs by chance due to sampling fluctuation. As the null hypothesis is accepted so this difference is not significant. Thus we conclude that the difference is a result of the sampling error.

So option 4 is the correct answer.

orchestra answered 2 years ago

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