Question

Painkillers and Miscarriage Exercise A.50 on page 179 describes a study examining the link between miscarriage and the use of painkillers during pregnancy. Scientists interviewed 1009 women soon after they got positive results from pregnancy tests about their use of painkillers around the time of conception or in the early weeks of pregnancy. The researchers then recorded which of the pregnancies were successfully carried to term. The results are in Table \(7.30 .\) (NSAIDs refer to a class of painkillers that includes aspirin and ibuprofen.) Does there appear to be an association between having a miscarriage and the use of painkillers? If so, describe the relationship. If there is an association, can we conclude that the use of painkillers increases the chance of having a miscarriage? 7.44 Binge Drinking The American College Health Association - National College Health Assessment survey, \({ }^{17}\) introduced on page 60 , was administered at 44 colleges and universities in Fall 2011 with more than 27,000 students participating in the survey. Students in the ACHA-NCHA survey were asked "Within the last two weeks, how many times have you had five or more drinks of alcohol at a sitting?" The results are given in Table 7.31 . Is there a significant difference in drinking habits depending on gender? Show all details of the test. If there is an association, use the observed and expected counts to give an informative conclusion in context. $$ \begin{array}{l|rr|r} \hline & \text { Miscarriage } & \text { No miscarriage } & \text { Total } \\\ \hline \text { NSAIDs } & 18 & 57 & 75 \\ \text { Acetaminophen } & 24 & 148 & 172 \\ \text { No painkiller } & 103 & 659 & 762 \\ \hline \text { Total } & 145 & 864 & 1009 \\ \hline \end{array} $$

Short answer

For the first problem, there appears to be an association between painkiller use during pregnancy and miscarriage, particularly for NSAIDs. However, a causal relationship cannot be determined from this analysis alone. For the second problem, the conclusion will depend on the results of the hypothesis test which might show whether there is a significant difference in drinking habits among genders.

Step-by-step solution

Understand the contingency table for the first problem

The contingency table for the first problem presents the frequency of miscarriage and no miscarriage for three groups of women: those who took NSAIDs, those who took Acetaminophen, and those who took no painkillers. The 'Total' row and column provide the total counts for each row and column.

Analyze the association

To determine if there is an association between painkiller use and miscarriage, we can calculate the proportion of miscarriages in each group. For NSAIDs, \(\frac{18}{75} = 0.24\) or 24%, for Acetaminophen, \(\frac{24}{172} = 0.14\) or 14%, and for no painkillers, \(\frac{103}{762} = 0.14\) or 14%. These proportions appear to be different, indicating a probable association between the type of painkiller used and the likelihood of miscarriage, with a higher proportion of miscarriages amongst those taking NSAIDs.

Interpret the association

While there is evidence of an association between the type of painkiller used and the likelihood of miscarriage, one cannot make a causal conclusion based solely on these data. There could be other factors, known as confounding factors, that also influence the observed association. This requires further investigation and potentially a controlled experiment where these other factors are controlled or adjusted for.

Understand the contingency table for the second problem

To solve the second problem, a contingency table similar to the one in the first problem should be present. It would show the count of students who participated in binge drinking within two weeks according to gender.

Formulate the Hypothesis

Based on the drinking habits data, a hypothesis test should be performed to analyze if there is a significant difference between the proportions of male and female students who binge drink. The null hypothesis is 'The proportion of male students who binge drink is equal to the proportion of female students who binge drink'. The alternative hypothesis is 'The proportion of male students who binge drink is not equal to the proportion of female students who binge drink'.

Conduct the Hypothesis Test

To conduct this test, calculate the proportions and standard errors. Then calculate the test statistic based on the difference between the proportions divided by the standard error. Obtain the p-value by comparing the test statistic to a standard normal distribution. A small p-value (<0.05 as a common threshold) would lead to the rejection of the null hypothesis in favor of the alternative hypothesis.

Conclude the test and provide an interpretation

Based on the p-value result, you will make a decision regarding the null hypothesis. If p-value is less than 0.05, you reject the null hypothesis which means there is a significant difference in drinking habits depending on gender. Otherwise, you can't reject the null hypothesis which means there is no significant difference. Then, use the observed and expected counts to give an informative conclusion in context.