The 2022 General Social Survey contains information on the number of hours worked by a respondent each week. The mean number of hours worked per week is 40.84, with a standard deviation of 16.72. The sample size is 361.

Estimate the value of the standard error .

Calculate a 90 percent confidence interval for these data .

Provide a one or two sentence interpretation of this result .

Using this data, provide a hypothetical numerical example which demonstrates that the precision of a confidence interval is in part a function of sample size .

Using this data, provide a hypothetical numerical example which demonstrates that the precision of a confidence interval is a function of both sample size and the level of confidence?