To address this problem about determining whether there is a difference between women and men in the average relationship length, here’s how you can approach it:

Which test should you use?

The appropriate statistical test to compare the average relationship length between men and women would be a two-sample t-test. This is because we are comparing the means of two independent groups (men and women), and the goal is to determine if there is a statistically significant difference between their average relationship lengths.

Reporting the absolute value of the test statistic:

Once you conduct the t-test, you will get a t-statistic. The problem asks for the absolute value of the test statistic, so you would report the positive value regardless of the sign.

Reporting the p-value:

The p-value tells you the likelihood of obtaining the observed results if the null hypothesis is true (i.e., that there is no difference in relationship lengths). You should report this p-value to at least 3 decimal places.

Conclusion:

If the p-value is less than a typical significance level (e.g., 0.05), you would reject the null hypothesis and conclude that there is a statistically significant difference between men and women in terms of average relationship length. If the p-value is greater than the significance level, you would conclude that there is no significant difference.

Would you like further details on how to calculate the t-test and p-value, or how to interpret them?

Here are 5 related questions you might explore:

1. What are the assumptions of a two-sample t-test?
2. What is the null hypothesis in this context?
3. How would you interpret the results if the test was not significant?
4. What are some alternatives to the t-test if the data do not meet the assumptions?
5. How would the results change if you conducted a paired t-test instead?

Tip: Always check whether your data meets the assumptions for the t-test, including normality and equal variance. If not, consider using a non-parametric test like the Mann-Whitney U test.