I need help with this question.

A survey asked the question: "For how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions, not good?" Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.10 to 4.24 days in 2010. (a) Interpret this interval in context of the data. We are % confident that US residents experienced poor mental health to days per month. (b) What does "95% confident" mean? Explain in the context of the application. 95% of random samples of size will yield a confidence interval that contains the true average number of bad mental health days that US residents experience per month. (c) Suppose the researchers think a 99% confidence level would be more appropriate for this interval. Will this new interval be smaller or larger than the 95% confidence interval? To be more sure they capture the actual mean, they require a [larger interval. (d) If a new survey were to be done with 500 Americans, would the standard error of the estimate be larger, smaller, or about the same? Assume the standard deviation has remained constant since 2010. Less data means less x precision, so the standard error would be larger