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

Assuming that the sample variance is s² = 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 α = .05?

Assuming that the sample variance is s² = 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 α = .05?

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