In the sample, there were there were 12 women in a relationship and 12 women who were not. For the women in a relationship, the sample mean baseline ocytocin level was 4.80433 pg/mL, and the sample standard deviation of the oxytocin levels was 0.33857 pg/mL. For the women who were not in a relationship, the sample mean baseline ocytocin level was 4.62958 pg/mL, and the sample standard deviation of the oxytocin levels was 0.19455 pg/mL. The data within each group was approximately symmetrically distributed and there were no apparent outliers.

Based on this information, one can perform a hypothesis test to answer the research question proposed above. In other words, we should test the null hypothesis that the mean (baseline) oxytocin level is the same for women whether they are in a relationship or not, against the alternative hypothesis that the two groups have different mean oxytocin levels. I.e. H₀: ₁- ₂= 0 vs H_a: ₁- ₂ 0, where ₁is the mean oxytocin level of women in the population who are in a relationship, and ₂is the mean oxytocin level of women in the population who are not in a relationship.

Use relevant formulae to determine the value of the test statistic. Then use R to produce the corresponding p-value for this test. You are likely to find the following function useful: pt(t,d), which gives the area to the left of a value t under a t-distribution with d degrees of freedom. For example, pt(-2,12) returns 0.03432751. Note that this function will not directly give you the answer to this question - you need to think about what you need to work out and what the function offers you. Sketching a t-distribution and thinking about the area you need (the p-value) may help. As an exercise after you have finished all three questions, attempt to work out the p-value (range) using statistical tables.