In 2020, it was reported that the mean salary of the highest paid parent or guardian in a household in MD was $42,000. You think that this could not possibly be true. You randomly choose 45 students at Eastern Tech and ask them about the highest salary in their household. The sample mean was $46,210 with a sample standard deviation of $3,842.

a) Is there some evidence that the mean salary of the highest paid parent/guardian in the household is different than $42,000? Explain

b) Is there convincing evidence that the mean salary of the highest paid parent/guardian is different than $42,000? Show all work.

c) Based on your conclusion above, identify the type of error that could occur AND describe that error in the context of the problem. No consequence is needed for this problem.

d) Construct a 95% confidence interval for the mean salary. No need to do the 4-step process(You already did it above), just calculate the confidence interval usign the calculator. What information can be concluded from the CI in relation to your ST?