QM PREREQ6 Basics of hypothesis testing

Question 1

Under what conditions do we reject the null hypothesis in a one tailed test?

Answer 1

When the absolute value of the test statistic is greatr than the absolute value of the critical value

Question 2

What is the formula for the critical value?

Answer 2

One tailed test:
tsubalpha / 2 or zsubalpha / 2

Two tailed test:
tsubalpha or zsubalpha

Question 3

Under what conditions do we reject the null hypothesis in a two tailed test?

Answer 3

right tail: relect null hypothesis when test statistic is greater than the critical value

left tail: reject when test statistic is less than the critical value

Question 4

What is the excel function call for a 2.5% right tail test?

Answer 4

NORM.S.INV(0.975)

Question 5

What is the excel function call for a 5% left tail test?

Answer 5

NORM.S.INV(0.05)

Question 6

How would we use confidence intervals to reject the null hypothesis?

Answer 6

If we determine xbar and the mu null population mean is outside the confidence interval range around xbar, we reject the null hypothesis

Question 7

What is the formula for confidence interval?

Answer 7

+- t x [s / sqrt(n)]

Question 8

Why would something statistically significant not be economically significant?

Answer 8

accounting for transaction costs, taxes and risk

Question 9

When do we accept the null hypothesis?

Answer 9

Never. We either reject the null based on the evidence or FAIL to reject the null

Question 10

What is the p-value?

Answer 10

The area in the probability distribution OUTSIDE the calculated test statistic.

Question 11

What is the p value for a two sided test statistic?

Answer 11

The probabilities under the curve in both tails beyond the calculated test statistic, added together

Question 12

What is the lowest alpha at which the null can be rejected?

Answer 12

The p-value

Question 13

What is the false discovery rate?

Answer 13

The expected proportion of false positives (at a given p value)

Question 14

What is the multiple testing problem?

Answer 14

In m repeated tests with a level of significance alpha, expect to generate m x alpha false positives.

Question 15

Why might we adjust the p value when conducting multiple tests?

Answer 15

false positives. in m repeated tests with level of significance alpha, m x alpha false positives can be expected

Question 16

How do we adjust alpha to eliminate false positives?

Answer 16

1. divide alpha by number of tests
2. Rank each significant test result by smallest to largest p
3. multiply alpha/number of tests by the rank
4. if p-value for that test is lower, keep
5. If p- value is greater, discard

The number remaining will tell you the NUMBER of false positives you would expect from the iterative tests.

Question 17

If we are using a 5% two tailed t test at what t value should we fail to reject the null hypothesis?

Answer 17

Less than an absolute value of 1.96
This applies for any sample size

Question 18

What is the test statistic for a chi-square test?

Answer 18

chi square subn-1 = [(n-1] x sample variance^2] / population variance

Question 19

Why can’t you use 1 - upper p to find the lower chi square critical value?

Answer 19

The chi square distribution is not symmetrical. Upper and lower tails are different shapes