代做Business Statistics代做留学生Matlab编程

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 H_a: 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, H_a: µ ≠ 85, x = 78, s = 25, n = 25