Final answer:
To determine plausible values for the population proportion (p) based on a 95% confidence interval of 0.72 to 0.79, we check if each value falls within the interval. The values given, 0.85, 0.75, 0.07, and 0.738, are all outside the interval and thus considered not plausible.
Step-by-step explanation:
The student's question pertains to interpreting a confidence interval for a population proportion and identifying which values are plausible based on that interval. The given 95% confidence interval for a proportion is 0.72 to 0.79. This means that based on the sample data and the confidence interval calculation, the true population proportion (p) is estimated to be between 0.72 and 0.79 with 95% confidence.
We assess the plausibility of each proposed value by determining whether it falls within this interval or not. Value a, which is 0.85, is not within the interval, so it is not plausible. Value b, which is 0.75, just barely falls outside the interval and is not considered plausible for a strict interpretation. Value c, which is 0.07, is significantly outside the interval and therefore not plausible. Lastly, value d, which is 0.738, is also not within the interval. The only plausible value would be within the confidence interval range of 0.72 to 0.79.