34.A group of 80 people who had been diagnosed as prediabetic because of high blood glucose levels volunteered to participate in a study designed to investigate the use of cinnamon to reduce blood glucose to a normal Of the 80 people, 40 were randomly assigned to take a cinnamon tablet each day and the other 40 were assigned to take a placebo each day. The people did not know which tablet they were taking. Their blood glucose levels were measured at the end of one month . The results showed that 14 people in the cinnamon group and 10 people in the placebo group had normal blood glucose levels. For people similar to those in the study, do the data- provide convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon? (A) No conclusion can be made about the use of cinnamon because the people in the study were volunteers. (B) There is convincing statistical evidence at the level of 0.01 . (C) There is convincing statistical evidence at the level of 0.05 but not at the level of 0.01 . (D) There is convincing statistical evidence at the level of 0.10 but not at the level of 0.05 . (E) There is not convincing statistical evidence at any reasonable significance level.

## Step 1<br />The problem involves a statistical hypothesis test. The null hypothesis is that the proportion of people who would be classified as normal after one month of taking cinnamon is equal to the proportion who would be classified as normal after one month of not taking cinnamon. The alternative hypothesis is that the proportion of people who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon.<br /><br />## Step 2<br />The data provided in the problem are:<br />- Number of people in the cinnamon group: 40<br />- Number of people in the placebo group: 40<br />- Number of people in the cinnamon group with normal blood glucose levels: 14<br />- Number of people in the placebo group with normal blood glucose levels: 10<br /><br />## Step 3<br />We can calculate the observed proportion of people with normal blood glucose levels in each group:<br />- Proportion in the cinnamon group: \( \frac{14}{40} = 0.35 \)<br />- Proportion in the placebo group: \( \frac{10}{40} = 0.25 \)<br /><br />## Step 4<br />The difference in proportions is \( 0.35 - 0.25 = 0.10 \).<br /><br />## Step 5<br />To determine if this difference is statistically significant, we would typically perform a hypothesis test. However, the problem does not provide the sample size for the entire population, which is necessary to calculate the standard error and perform the test.<br /><br />## Step 6<br />Given the information, the most appropriate answer is (E) "There is not convincing statistical evidence at any reasonable significance level." This is because we cannot determine the statistical significance of the difference in proportions without additional information about the sample size.