What confidence interval will have the larger margin of error when using the same sample data and why? A 95% confidence interval or a 90% confidence interval?

Suppose we take a survey of 400 students and ask how much they study per week. The result is an average of 8.5 hours per week. The 95% confidence interval is (8, 9). What does the confidence interval mean in this context?

How can we interpret a 95% confidence interval?

You're considering going to graduate school, and you would like to know how many people would recommend it. You talk to 28 people, and 6 recommend it. Construct a 96% confidence interval for p, the proportion of people that recommend you go to graduate school. What is the lower bound of this interval?

We plan to sample parents in order to construct a 99% confidence interval for the proportion who believe that physical education has a positive effect on academic performance. Estimate the sample size needed so that a 99% confidence interval will have a margin of error of 0.025.

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.3%, 5.1%). What is the point estimate of the mean percentage of reservations that are canceled on the day of the flight?

What is the difference between the different confidence interval formulas?

You're considering going to graduate school, and you would like to know how many people would recommend it. You talk to 30 people, and 7 recommend it. Construct a 96% confidence interval for p, the proportion of people that recommend you go to graduate school. What is the lower bound of this interval?

A study was being done to estimate the proportion of students who receive financial aid. If the study would like to construct 90% confidence interval for the proportion of students receiving financial aid within 2%, what sample size would be needed? A previous study stated that 53% of students receive some form of financial aid.

Treating the 2015 Tobacco rate data as a sample, construct a 95% confidence interval for the mean tobacco rate for males and for females. Interpret each interval. Does it appear that males use tobacco at a higher rate than females? Justify your answer, using the confidence intervals in your explanation. Construct the same confidence interval for males at the 99% confidence level. Compare to the male 95% confidence interval from the previous question. What happened to the interval when the confidence level increased? Explain why. Prevalence of smoking any tobacco product among persons aged >= 15 years Male 2015 Prevalence of smoking any tobacco product among persons aged >= 15 years Female 2015 51.2 7.6     37.2 27.8         29.5 18.4 52.3 1.5 16.7 13.1 35.5 34.8 46.5 0.4     48.8 7.6 39.8 0.7 13.1 0.9 46.2 10.6 26.5 20     17.7 1     30.5 17.1 47.2 30     19.3 11.3 29.3 3.1 42.4 28.2 36 4.5         22.2 3.5 44.1 2.8…