I am having diffuclty with these two questions on my statistics hw. Thanks!

Show complete steps for the hypothesis tests of population mean and population proportion

Exercise 1:

National Motors would like to claim that their new brake system achieves a shorter mean stopping distance than the 60 ft claimed by a competitor. Use a hypothesis test at = 0.05 to support their claim. A random sample of 81 cars have a mean of 57.90 ft and a standard deviation of 6.13 ft.

Exercise 2:

Suppose we wish to prove that a majority of market researchers believe that a certain survey method is unethical. A random sample of 205 shows 117 believe the method is unethical. We will assume that 50% believe the method is unethical and that any apparent difference from 50% is just random fluctuation. Test the hypothesis about the unethical proportion.

a) If the significance level is set to be 0.05, what is your conclusion? Why?

b) If the significance level is set to be 0.01, what is your conclusion? Why?