A recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say "I love you." For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say "I love you" first.

1. Identify the observational units and variable in this study. Also classify the variable as categorical or quantitative.
2. State the appropriate null and alternative hypotheses (in words) for testing whether males are more likely to say "I love you" first.

We can express these hypotheses with symbols as:

Null:

=

0.50

=0.50

Alternative:

>

0.50

>0.50

1. Describe (in words) what the symbol
3. stands for here.

It turned out that for 28 of the 40 couples in the sample (after the 7 couples who could not agree were excluded), the man said "I love you" before the woman did.

1. Determine the sample proportion (written as a decimal) of couples for whom the man was the first to say "I love you." What symbol do we use to denote this proportion?
2. Describe how you could use a coin-flipping model to find the p-value for these data.
3. Use an applet to conduct a simulation analysis to assess the strength of evidence against the null hypothesis provided by the sample data. Report the values that you enter into the applet and describe how you approximate the p-value. Also report the value of this (approximate) p-value.
4. Write a sentence or two interpreting this p-value: the probability of ______, assuming ______.
5. Summarize your conclusion from this p-value.