# Statistics: Testing a Null Hypothesis

A researcher is testing a null hypothesis that states: Ho: = 50. A sample of 25 scores is selected and the mean is M = 55.

Assuming that the sample variance is 100, compute the estimated standard error and the t statistic. Is this sample sufficient to reject the null hypothesis using a two-tailed test with alpha = .05?

Assuming that the sample variance is 400, compute the estimated standard error and the t statistic. Is this sample sufficient to reject the null hypothesis using a two-tailed test with alpha = .05?

Explain how increasing variance affects the standard error and the likelihood of rejecting the null hypothesis.

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#### Solution Preview

With alpha = 0.05 and degree of freedom=n-1=25-1=24 and also a two-sided test, the t-statistic=2.064 by t table.

So if the sample variance is 100, then the estimated ...

#### Solution Summary

An explanation of how increasing variance affects the standard error and the likelihood of rejecting the null hypothesis.