Hypothesis Testing

Question 1

Hypothesis

Answer 1

Statement about one or more populations

Question 2

Steps of hypothesis testing

Answer 2

1. State hypothesis
2. Identify appropriate test statistic and its probability distribution
3. Specify significance level
4. State decision rule
5. Collect data and calculate test statistic
6. Make statistical decision
7. Make economic or investment decision

Question 3

Describe and interpret choice of null and alternative hypotheses

Answer 3

Null - hypo to be tested
Alt - hypo accepted when null rejected (set up as suspected condition with one-sided test, or for neutrality use two-sided)

Question 4

One tailed vs. two tailed tests

Answer 4

One tail - equals hypothesis (could be bigger or smaller)

Two tail - greater/less than or equal to hypothesis (halve significance level)

Question 5

Test statistic

Answer 5

Quantity, calculated based on sample, whose value is basis for deciding whether or not to reject the null hypothesis

(sample statistic - value of hypo population parameter) / standard error of sample statistic

Std error = std dev / square root n

Question 6

Type I error

Answer 6

Reject true null hypo. α is prob of type I error.

Question 7

Type II error

Answer 7

Not reject false null hypo. β is prob of type II error.

Question 8

Significance level and how used in hypothesis testing

Answer 8

Probability of committing a type I error - denoted with α

Question 9

Decision rule

Answer 9

If test statistic is more extreme than given value based on certain significance level, reject null hypothesis

Question 10

power of a test

Answer 10

Probability of correctly rejecting the null (inverse of significance level)

Question 11

relationship of confidence intervals and hypothesis tests

Answer 11

In two tailed tests, (1-α) confidence intervals and hypothesis tests will produce the same results

Question 12

Distinguish between statistical result and economically meaningful result

Answer 12

Statistically significant result requires rejection of null hypothesis

Question 13

Explain and interpret p-value as it relates to hypothesis testing

Answer 13

Smallest level of significance at which null hypothesis can be rejected. Smaller the p-value, stronger the evidence against the null hypothesis (i.e. more sure of rejecting)

Question 14

Test statistic and results interpretation re population mean of both large and small samples when population is normally or approximately distributed and variance KNOWN

Answer 14

z = x-μ / (σ / sq rt n)

Question 15

Test statistic and results interpretation re population mean of both large and small samples when population is normally or approximately distributed and variance UNKNOWN

Answer 15

t (sub n-1) = X-μ / (s / sq rt n)

Question 16

Test statistic and results interpretation re equality of population means of two at least approximately normally distributed populations based on independent random samples with EQUAL assumed variances

Answer 16

t = (x1-x2) - (μ1-μ2)
___________
(PE/n1+PE/n2)^1/2

PE = (n1-1)s1^2 + (n2-1)s2^2
_________________
n1+n2-2

df = n1+n2-2

Question 17

Test statistic and results interpretation re equality of population means of two at least approximately normally distributed populations based on independent random samples with UNEQUAL assumed variances

Answer 17

Same t test formula, but use standard deviation in place of the pooled estimator. CALCULATE TEST STATISTIC FIRST b/c whether it’s significant might be obvious.

df = (s1^2/n1 + s2^2/n2) ^2
_________________
[(s1^2/n1)^2]/n1 + [(s2^2/n2)^2/n2

Question 18

Test statistic and results interpretation re mean difference of two normally distributed populations (SAMPLES DEPENDENT)

Answer 18

t = d - μ
____
s

df = n-1
d = sample mean difference

Question 19

Test statistic and result interpretation re variance of normally distributed population

Answer 19

χ^2 = (n-1)s^2
______
σ^2

Chi square test requires random sample and normally distributed population

df = n - 1

For less than hypotheses, lower α point is (1-α) on chi square chart

Question 20

Test statistic and result interpretation re equality of variances of two normally distributed populations based on two independent random samples

Answer 20

F = sample1 variance / sample2 variance [FLIP TO LARGER]

df1 = n1-1
df2 = n2-1

Not equal to - reject if greater than upper α/2 point of f-distribution

greater/less than - reject if greater than upper α point of f-distribution

Question 21

Parametric vs. nonparametric tests and when appropriate

Answer 21

Parametric tests concern parameters and rely on assumptions

Nonparametric tests not concerned with parameters or has minimal assumptions. Use when: data do not meet distributional assumptions, data given in ranks, when hypothesis addressing does not concern parameter

Question 22

t-distribution

Answer 22

Symmetrical distribution defined by single parameter: degrees of freedom. Fatter tails than normal distribution.