HW 9 (16 points total)
1. Are the following statements true or false? Explain. (4 points)
a. As the significance level increases, the probability of a Type I error increases.
b. The power is equal to one minus the probability of a Type II error
c. As the power increases, the probability of a Type II error decreases.
d. As the significance level increases, the size of the rejection region increases.
2. A random sample of 49 observations from a normal population yields a sample mean of 85. The population standard deviation is 14 and the significance level is 5%. Conduct the hypothesis testing on the claim that the population mean is greater than 85. (4 points)
3. Test H0: µ = 10 versus Ha: µ ≠ 10 using the p-values. Assume that x = 12, σ = 4, the significance level is 5%, and n = 36. (4 points)
4. Find the t statistic and carry out the statistical test for the following situations in sampling data from a normally distributed population. Use a significance level of .05. (4 points)
H0: µ = 85, Ha: µ ≠ 85, x = 78, s = 25, n = 25