A popular claim nicknamed "freshman 15" states that many college students gain weight in their freshman year. You are give 95% confidence interval as 55.9% < p < 78.4%. correctly interpret the interval.
The answer is D. We are 95% confident that the interval from 55.9% to 78.4% actually does contain the true percentage of college freshmen who gain weight
The 95% confidence interval, given as 55.9% < p < 78.4%, suggests that we can be 95% confident that the true proportion of college students who gain weight in their freshman year falls within this range.
In other words, based on the sample data and statistical analysis, we estimate that the percentage of college students who experience weight gain in their freshman year is between 55.9% and 78.4%. However, we cannot say with certainty the exact percentage, but we can be reasonably confident that it falls within this range.
To correctly interpret the given confidence interval of 55.9% < p < 78.4% in the context of the "freshman 15" claim, we need to understand what it represents.
A confidence interval is a range of values that is likely to contain the true population parameter. In this case, the parameter of interest is the proportion of college students who gain weight in their freshman year. The confidence interval suggests that the true proportion falls somewhere between 55.9% and 78.4%.
Specifically, this means that if we were to select multiple random samples of college students and calculate the proportion of those who gained weight in each sample, 95% of the calculated confidence intervals would contain the true proportion of the entire population.
For example, if we were to repeat the study many times, about 95% of the time, the calculated confidence intervals would include the true proportion of college students who gain weight in their freshman year. However, it is important to note that we cannot say with certainty that the true proportion lies within this particular interval (55.9% to 78.4%) because there is still a small chance (5%) that the true proportion lies outside this range.
In conclusion, based on the given confidence interval, we can infer that there is strong evidence to suggest that the proportion of college students who gain weight in their freshman year is likely to be between 55.9% and 78.4%.
connexus stats quiz
1. A
2. A
3. A
4. B
5. C
6. A
7: D
8. D
9. D
10. C