A political science professor is interested in comparing the...

A political science professor is interested in comparing the characteristics of students who do and do not vote in national elections. For a random sample of 114 students who claimed to have voted in the last presidential election, she found a mean grade point average of 2.71 and a standard deviation of 0.64 . For an independent random sample of 123 students who did not vote, the mean grade point average was 2.79 and the standard deviation was 0.56. Test, against a twosided alternative, the null hypothesis that the population means are equal.

Key Concepts

Two-Sided Test

A two-sided test considers deviations in both directions from the hypothesized value, meaning that the alternative hypothesis includes both possibilities of the first mean being larger or smaller than the second mean. This approach is used when there is no prior assumption about the direction of the difference.

Degrees of Freedom

Degrees of freedom in a t-test refer to the number of independent pieces of information available for estimating parameters. They affect the shape of the t-distribution used to determine critical values and p-values for hypothesis testing.

Test Statistic

The test statistic, often a t-statistic in this context, measures the standardized difference between the sample means. It is computed by taking the difference between the means and dividing it by the standard error of the difference, reflecting the magnitude of the observed difference relative to the variability in the data.

Alternative Hypothesis

The alternative hypothesis is the statement that contradicts the null hypothesis. When comparing two means, it states that there is a difference between the groups. A two-sided alternative does not specify the direction of the difference, only that it exists.

Null Hypothesis

The null hypothesis is a default assumption that there is no effect or no difference between groups. In the context of comparing two population means, it posits that the means are equal, and any observed difference in the sample is due to random chance.

Hypothesis Testing

Hypothesis testing is a systematic method used in statistics to make decisions using experimental data. It involves stating a null hypothesis and an alternative hypothesis, then using a test statistic to evaluate whether the data provide enough evidence to reject the null hypothesis in favor of the alternative.

Independent Samples t-Test

An independent samples t-test is used to compare the means of two independent groups to determine if there is statistically significant evidence that the respective population means differ. It accounts for sample size and variability in each group.

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