1. A study looked at 254 heterosexual couples where the female partner had cancer. Of those couples, 53 ended up in divorce.
The researchers know from other studies that when the male partner gets cancer, 3 percent of couples end up in divorce.
Test the null hypothesis that in the population of heterosexual couples where the woman gets cancer, 3 percent of them end up in divorce. Assume alpha = .05.
a. Write the null and alternative hypotheses, using the mathematical notation discussed in class.
b. Write the null and alternative hypotheses in words. Make clear these hypotheses refer to the population.
c. Calculate the proportion of couples (with female cancer patients) that got divorced in the sample.
d. Calculate the critical values. These are the z-scores that bound the middle 95 percent of the normal distribution. Use the 68-95-99.7% rule.
e. Calculate the standard error, assuming the null hypothesis is correct.
f. Calculate the test statistics. Remember, you will have both a positive and negative version of the test statistic.
g. Which is farther away from zero, your test statistics or your critical values?
h. Is your P-value less than .05, or greater than it?
i. Do you reject the null hypothesis or retain it?