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Question 4 please although I am unsure of my answers for the rest as well :(...

Question 4 please although I am unsure of my answers for the rest as well :(

Here is the full list for background info.

  1. Consider a significance test for a null hypothesis versus a two-sided alternative. State all values of a standard normal test statistic z that will give a result significant at the 10% level but not at the 5% level of significance. (Sec. 6.2)

  1. You perform 1,000 significance tests using α = 0.01. Assuming that all the null hypotheses are true, how many of the test results would you expect to be statistically significant? Explain your answer. (Sec. 6.3)

  1. One way to deal with the problem of misleading P-values when performing more than one significance test is to adjust the criterion you use for statistical significance. The Bonferroni correction procedure for k independent hypothesis tests at an overall level of significance α requires conducting each individual test at the α/k level of significance. You perform 5 independent tests of significance and observe the following     P-values: 0.0773, 0.0524, 0.0308, 0.0127, and 0.0098. Which of these tests are statistically significant using the Bonferroni correction procedure with α = 10%. (Sec. 6.3)

  1. You must decide which of two discrete distributions a random variable X has. We will call the distributions p0 and p1. Here are the probabilities they assign to the values x of X.

x

-2

-1

0

1

2

p0

0.20

0.20

0.20

0.20

0.20

p1

0.05

0.25

0.30

0.25

0.15

You have a single observation on X and wish to test

                    H0: p0 is correct

                            versus

                    H1: p1 is correct.

One possible decision procedure is to reject H0 if X ≤ 0. (Sec. 6.4)

  1. Find the probability of a Type I error, that is, the probability that you reject H0 when p0 is the correct distribution.

  1. Find the probability of a Type II error.

  1. Find the power of the test procedure.

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