{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ECON301_Handout_06_1213_02

# Hypothesis whereas a type ii error consists in

This preview shows pages 9–14. Sign up to view the full content.

hypothesis, whereas a Type II error consists in accepting a false hypo thesis. The symbol α is also known as the size of the (statistical) test.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
ECON 301 - Introduction to Econometrics I April, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 10 If ˆ i t falls in the critical region (or rejection region), we reject the null hypothesis, that is, we say that the estimate of 1 is statistically significant. If ˆ i t falls in the acceptance region, that is to say if (taking the desired level of significance as 0.05) 0.025 0.025 ˆ i t t t (with T-k-1 degrees of freedom), we accept the null hypothesis, that is, we conclude with a probability of 95 percent that our estimate of 1 is not statistically significant. The acceptance and critical regions for 10 degrees of freedom and 0.05 level of significance are shown in Figure below ( ˆ 2.228 2.228 i t ).
ECON 301 - Introduction to Econometrics I April, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 11 t Test: Decision Rules for Two Sided Test Type of hypothesis H 0 : the null hypothesis H 1 : the alternative hypothesis Decision rule: reject H 0 if Two-tail * ii  * /2, df tt Notes: * i is the hypothesized numerical value of i . | t | means the absolute value of t . /2 t means the critical t value at the α level of significance. df : degrees of freedom, (T − 2) for the two-variable model (including intercept), (T – k –1) for the k independent variable model (including intercept). Example 1 Suppose that from a sample of size T =20, we estimate the following consumption function: ˆ 160.2 0.70 CY  (75.5) (0.21) The figures in parenthesis are the standard errors of the coefficients. For individual significance test of intercept term, we wish to test the hypothesis 00 :0 H Against the alternative hypothesis 0 A H The t statistic for slope coefficient is as follows:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
ECON 301 - Introduction to Econometrics I April, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 12 0 0 ˆ 0 ˆ 160.2 2.12 75.5 ˆ () t se Taking the level of significance as 0.05 ( =0.05), the critical values of t for T-k-1=20-1-1=18 degrees of freedom are: -t 0.025 =-2.101, and t 0.025 =2.101. Hence the acceptance region 0 0.025 0.025 ˆ t t t is 0 ˆ 2.101 2.101 t . Since, 0 0.025 ˆ tt , we reject the null hypothesis and conclude that the estimate of 0 is statistically significant from zero at 0.05 level of significance. For individual significance test of slope coefficient, we wish to test the hypothesis 01 :0 H Against the alternative hypothesis 1 A H The t statistic for slope coefficient is as follows: 1 1 ˆ 1 ˆ 0.7 3.3 0.21 ˆ t se Taking the level of significance as 0.05 ( =0.05), the critical values of t for T-k-1=20-1-1=18 degrees of freedom are: -t 0.025 =-2.101, and
ECON 301 - Introduction to Econometrics I April, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 13 t 0.025 =2.101. Hence the acceptance region 1 0.025 0.025 ˆ t t t is 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page9 / 17

hypothesis whereas a Type II error consists in accepting a...

This preview shows document pages 9 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online