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Hypothesis Testing (Chapter 3,

up to page 53)

• Remember we don’t see the true line
  • So we don’t know the true intercept or the slope coefficients.
• We collect a sample.
• We use OLS to estimate the coefficients.
• Hypothesis testing refers to using sample

information to draw a conclusion about the

true population coefficient.

Four Steps of Hypothesis

Testing

Step One

• Set the null and alternative hypotheses

about the true coefficients.

• Alternative hypothesis is consistent with our common sense or theory. It is what we expect to find. It is what we expect to fail to reject.
• Null hypothesis is what we expect to not find. It is what we expect to reject.

Two Sided Hypotheses

• Suppose all you want to show is that something affects something else. But you don’t want to show the direction of the relationship
• In this case, you will set a two sided hypothesis
• Example
  • All you want to show is that calorie intake does affect the weight.
  • In this case you would set up a two sided test.

Suppose B 3 is the true coefficient

of calorie intake, then the two

sided hypothesis looks like this

You expect to

• Reject the null hypothesis H 0 in favor of

alternative hypothesis, H A

• And if you do,
• You have found empirical evidence that

calorie intake does matter.

• However, you are not making any

statements with regards to the nature of

the relationship between calorie in take

and weight.

One sided hypotheses

• Suppose you want to show that something

has a positive (or negative) effect on

something else. In this case, you will set a

one sided hypothesis

• Example
  • you want to show that calorie intake affect the weight in a positive way
  • In this case you would set up a one sided test

Suppose B 3 is the true coefficient of

calorie intake, then the one sided

hypothesis looks like this

• H 0 : B3 ≤
• H (^) A : B 3 >

You expect to

• Reject the null hypothesis H 0 in favor of alternative hypothesis, HA
• And if you do,
• You have found empirical evidence that calorie intakes have a positive effect on weight.
• Notes
  • A one sided test is stronger than a two sided test.
  • You must test a stronger hypothesis when possible.

Type I Errors

• Refers to rejecting a true null hypothesis
• Example
• Weight = ……..+ B3 calorie in take + error
  • H 0 : B 3 ≤
  • HA: B 3 >
• If you reject a true H 0 , you will conclude

that the higher the calorie intake the higher

the weight; while in reality, calorie intake

does not matter.

Type II Error

• Refers to failing to reject a false null hypothesis
• Example
• Weight = ……..+ B3 calorie in take + error
  • H 0 : B 3 ≤
  • HA: B 3 >
• If you fail to reject a false H 0 , you will

conclude that calorie intake does not

matter; while in reality, it does.

Type I/Type II Errors

B 3 is zero or negative

B 3 is positive

We conclude that B 3 is positive

Type I error No error

We conclude that B 3 is zero or negative

No error Type II error

Which type of error is more

serious?

• – Type I error: We conclude that the higher calorie in take, the height the weight. (While in reality there is no correlation between the two.) So we put a lot of effort into watching our calorie intake while we should not.
• – Type II error: We conclude that calorie intake does not affect the weight, while it actually does. So, we do not watch our diet. ( no effort )
• – When testing hypothesis we try to minimize type I error

Four Steps of Hypothesis

Testing

• Step Two
• Choose the level of significance (alpha)
  • Alpha measures the probability of rejecting a true null hypothesis (type I error)
  • The smaller alpha the smaller the probability of type I error
• Find the critical tc (page 312)
  • Degrees of freedom = n-k-
    • Where n=sample size, k= number of independent variables
• Formulate the decision rule

The decision rule

Otherwise, fail to reject the null hypothesis; where t = t-statistics

And t- stat is

B^ is the estimated B Bnullis the value of B under null hypothesis (usually zero) SE (B^) is the standard error of B^

Four Steps of Hypothesis Testing

• Step Three
• Estimate the regression equation and find

the t- statistic

• Formula (Page 48)
• T-stat. for the null hypothesis equal to zero

is reported by EViews.

Four Steps of Hypothesis

Testing

• Stop Four
• Apply the decision rule to either
  • Reject the null hypothesis
  • Or fail to reject the null hypothesis

Assignment 4

(Due before 10 PM on Wednesday, September 19, 30 points)

1. Set up the appropriate null and alternative hypotheses for our height- weight equation that we estimated before. Test your hypothesis at alpha = 10 percent. Don’t skip any steps. Evaluate your results. {Note: EViews output includes both the stand errors and the t-stats [for null hypotheses that have zero in them (=
   1. ≥0 or ≤0 ]}
2. #3, Page 61

3. 8, Page 62