Lorraine computed a confidence interval for μ based on a sample of size 41. since she did not know σ, she used s in her calculations. lorraine used the normal distribution for the confidence interval instead of a student's t distribution. will her interval be longer or shorter than one obtained by using an appropriate student's t distribution? explain.

Which of the following are independent events? a) knowing that it is going to rain tomorrow, and bringing an umbrella to schoolb) knowing that you have to get up early tomorrow, and going to bed before 9 p.mc) knowing that it is going to rain tomorrow, and going to bed before 9 p.md) knowing that you have a test in school tomorrow, and studying thw night before