Question

Physical activity and enhanced mood. Williams, Dunsiger, Jennings, and Marcus [2012] conducted a studyto test how enhanced mood during exercise can increase the like- lihood of physical activity in the future. They reported that at 6 months of physical activity, mood scores (rated on a scale from -5 to +5) after a walking exercise were 3.3 ± 1.2, and at 12 months, mood scores after a walking exercise were 3.3 ± 1.3 [mean ± standard error]. Assuming these data are normally distributed, use the steps to conduct a z transformation to determine the following probabilities:

(a) What is the probability that a sample mean selected from this population would show no change (0) or a negative change (less than 0) at 6 months of phys- ical activity?
(b) What is the probability that a sample mean selected from this population would show no change (0) or a negative change (less than 0) at 12 months of physical activity?

Answer 1

To determine the probability of no change or negative change in mood scores after 6 and 12 months of physical activity, a z transformation can be conducted. The probabilities are approximately 0.28% for 6 months and 0.62% for 12 months.

Step-by-step explanation:

To determine the probability of no change or negative change in mood scores after 6 and 12 months of physical activity, we can conduct a z transformation. The z transformation allows us to standardize the data and calculate probabilities based on the standard normal distribution.

1. For 6 months, we subtract the mean score (3.3) from 0 and divide by the standard error (1.2) to get the z score. This gives us a z score of -2.75.
2. Using a z-score table or a calculator, we can find the probability associated with a z-score of -2.75. The probability is approximately 0.0028 or 0.28%.
3. For 12 months, we follow the same steps and get a z score of -2.5. The probability associated with a z-score of -2.5 is approximately 0.0062 or 0.62%.