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Hypothesis Testing Flashcards

1
Q

The six-step process of Hypothesis Testing

A
  1. state the hypothesis
  2. identify the appropriate test statistic and its probability distribution
  3. specify the significance level
  4. state the decision rule
  5. collect data and calculate the test statistic
  6. make a decision
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2
Q

Null hypothesis

A
  • Ho
  • what the researcher wants to reject
  • contains the = component, <=, >=, =
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3
Q

Alternative hypothesis

A
  • Ha
  • what the researcher wants to prove
  • if Ho is rejected, the Ha is considered valid
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4
Q

What is the Ho and Ha for:

Supposed you are a researcher and believe that the average return on all Asian stocks was greater than 2%.

A
  • Ho: mue <= 2%

- Ha: mue > 2%

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5
Q

How to tell if a test will be left-sided or right-sided:

A

It comes down the the direction () of the Ha

  • Right-side, “mue is greater than 2%” (>)
  • Left-side, “mue is less than 2%” (
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6
Q

Left-side test symbol

A
  • Ha less than symbol

Ha = Mue < x.

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7
Q

Right-side test symbol

A
  • greater than

- Ha = Mue > x

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8
Q

Test statistic def

A
  • the test stat is calculated from sample data and compared to a critical value to decide whether or not we can reject the null hypotheses
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9
Q

Test stat of a population formula:

A

test stat = sample stat - value of the parameter under Ho / std error

= ^x - mue / std/squrt n

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10
Q

What is the test stat formula for:

Draw 36 observations from a population and get a sample mean of 4. we are told that the std of the population is 4. if the hypothesized value of the pop mean is 2, the test stat is:

A

test stat = ^x - mue / std error

4 - 2 / (4 / sq rt of 36) = 6

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11
Q

Level of Significance

A
  • reflects how much sample evidence is required to reject the null hypothesis
  • ie. a=5%, there is a 5% chance of rejecting a true null hypothesis
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12
Q

Type I error

A
  • we may reject a true null hypothesis

probability, significance level, a

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12
Q

Type I error

A
  • we may reject a true null hypothesis

probability, significance level, a

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13
Q

Type II error

A
  • we fail to reject a false null hypothesis
  • denoted as (B)
  • represents the probability of correctly rejecting the null when it is false
  • P test, 1 - P, ie 1 - B
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14
Q

If we decrease the probability of a Type I error by using a smaller significance level (ie use a=1% vs a=5%), we increase the probability of a Type II error.

A

The only way to reduce both types of errors is by increasing the sample size, n

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15
Q

The critical value is also known as the …

A
  • the rejection point for the test statistic

- a=5%, rejection point at z=1.645 on the bell curve

16
Q

p-value

A
  • “probability value”

- the smallest level of significance at which the null hypothesis can be rejected

17
Q

If the p-value is lower than our specified level of significance, we…

p-value < significance level

A
  • we reject the Ho, accept Ha
18
Q

If p-value is greater than our specified level of significance, we…

p-value > level of significance

A

we do not reject the null

19
Q

The power of test

A
  • correctly accepting Ha when Ho is false

- calculated as (1-B)

20
Q

The probability of a Type II error:

A
  • denoted as B (beta)
21
Q

Given a small sample (n<30) and Normal Distribution, which test is used when the variance is known?

A
  • z test when variance is known
22
Q

Given a small sample (n<30) and Normal Distribution, which test is used when the variance is unknown?

A
  • t-test when the variance is unknown
23
Q

Given a large sample (n>=30) and Normal Distribution, which test is used when the variance is known?

A
  • z test when variance is known
24
Q

Given a large sample (n>=30) and Normal Distribution, which test is used when the variance is unknown?

A
  • either a t-test or z-test will work with a large sample and unknown variance
25
Q

Given a small sample (n<30) and Non-Normal Distribution, which test is used when the variance is unknown?

A
  • NA
26
Q

Given a small sample (n<30) and Non-Normal Distribution, which test is used when the variance is known?

A
  • NA
27
Q

Given a large sample (n>30) and Non-Normal Distribution, which test is used when the variance is unknown?

A
  • t-test or z-test when the sample is large and variance is unknown for a non-normal distribution
28
Q

Given a large sample (n>=30) and Non-Normal Distribution, which test is used when the variance is known?

A
  • z-test when the sample is large and variance is known for a non-normal distribution
29
Q

A Chi-square test is used for:

A
  • tests concerning the variance of a normally distributed population
  • the graph is bound at zero
30
Q

A F-Test is used for:

A
  • testing the equality of two variances
  • graph is bound at zero

assumes:
- samples must be independent
- the populations from which the samples are taken are normally distributed

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