Hypothesis testing - Steps
Hypothesis testing - Steps
? Steps to do a two-tailed test of the hypothesis that 1 = 0: 1. Set up the hypotheses:
H0 : 1 = 0 Ha : 1 = 0.
2. Compute the test statistic:
t=
b1 - 0
= b1
Std. error of b1 ^b1
3. Read critical value off the t-table: t/2,n-2 4. Reach your conclusion: If |t| > critical value conclude Ha. If |t|
critical value, conclude H0 or fail to reject H0 at level .
Stat 328 - Fall 2004
1
One-tailed hypothesis tests
? We can also test one-sided or one-tailed hypothesis.
? A one-sided hypotheses would be:
H0 : 1 = 0 Ha : 1 > 0,
or Ha : 1 < 0.
? Steps are exactly the same, but now the critical value is t,n-2 (we do not divide into 2).
? If the test statistic |t| is larger than the critical value off the table and we conclude Ha, we would be concluding that 1 is larger (or smaller, depending on the test we set up) than zero.
Stat 328 - Fall 2004
2
Hypothesis testing (cont'd)
? If we wish to test a two-sided hypothesis about 1 at level we can also use the 100(1 - )% confidence interval to do so.
? We will conclude Ha whenever the CI does not include the hypothesized value for 1 (the value in H0).
? If the null hypothesis is H0 : 1 = 0, then we will reject the null at level when the CI does not contain the value zero.
? Why?
Stat 328 - Fall 2004
3
Hypothesis testing (cont'd)
? Note that the test of hypothesis (two-tailed) says: fail to reject H0 : 1 = 0 if
b1 - 0 ^b1
>
t
2
,n-2
or
b1 - 0 ^b1
<
-t
2
,n-2.
? Equivalently, by multiplying both sides of expressions above by ^b1 and subtracting b1 from both sides also, note that we fail to reject when
0
>
b1
-
t
2
,n-2^b1
and
0
<
b1
+
t
2
,n-2^b1
in other words, when 0 is inside the 100(1 - )% CI for 1.
? This applies only to two-sided tests.
Stat 328 - Fall 2004
4
Hypothesis testing (cont'd)
? JMP and SAS produce a p- value.
? The p- value is the smallest - level that still leads to rejecting H0.
? A p-value of 0.001 means that if I conclude Ha I only have a 1 in a thousand chance of reaching the wrong conclusion.
? A p- value of 0.3 means that if I conclude Ha I have a 1 in 3 chances of reaching the wrong conclusion.
? Typically we choose Ha only if the chance of making the wrong choice is small, say below 5%. Thus, p-values of 0.05 or smaller lead to Ha.
? The p- values produced by computer programs the test H0 : 1 = 0 versus Ha : 1 = 0.
Stat 328 - Fall 2004
5
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