Suppose a study is done in which several random samples of people from a population are taken and polled on the number of hours per night they sleep. It is determined that the sample proportion for those who sleep at least 8 hours a night is 36%, and the 95% confidence interval goes from 32% to 40%. Which of the following conclusions may be drawn based on this information alone?
What conclusions?
Based on the information provided, several conclusions can be drawn:
1. The sample proportion for those who sleep at least 8 hours a night is 36%. This means that, within the sample, approximately 36% of people reported sleeping at least 8 hours a night.
2. The 95% confidence interval for the population proportion goes from 32% to 40%. This means that we are 95% confident that the true population proportion of people who sleep at least 8 hours a night falls within the range of 32% to 40%.
3. Since the confidence interval includes the value of 36%, we can conclude that the sample proportion of 36% is a reasonable estimate of the true population proportion.
4. We can also conclude that within the population being studied, the proportion of people who sleep at least 8 hours a night is likely to be somewhere between 32% and 40% with 95% confidence.
However, it's important to note that drawing broader conclusions or making generalizations beyond the specific population being studied would require additional information or further analysis.