Question

Suppose that 10 sets of hypotheses of the form Ho:u= H H1: U* NO have been tested and that the P-values for these tests are 0.12, 0.09, 0.96, 0.02. 0.01, 0.05, 0.88,0.15, 0.14, and 0.07. Use Fisher's procedure to combine all of these P-values. What conclusions can you draw about these hypotheses? xo [Round your answer to 2 decimal places.]

Answer 1

Answer:

Given that:

Combine all known P-values using the Fisher's procedure

The test statistics $\chi ^2_0$ follows a chi square distribution with 2m degrees of freedom

The null and alternative hypothesis are

$H_0:\mu =\mu _0$

$H_1:\mu \neq \mu _0$

The specified level of significance is $\alpha$ =0.05

The chi square critical value at 0.05 level of significance with 2*10=20 degrees of freedom is 31.411

The formula for the $\chi ^2$ test statistic value

$\chi ^2_0=-2\sum_{i=1}^{m}ln(P_i)$ for all i=1,2,3,...m

Find the value of $\chi ^2$

Substitute all known P-values in the formula

$\chi _0^2=-2[ln(0.12)+ln(0.09)+ln(0.96)+ln(0.02)+ln(0.01)+ln(0.05)+ln(0.88)+ln(0.15)+ln(0.14)+ln(0.07)]$$\chi ^2_0=-2[-2.1202-2.4079-0.0408-3.9121-4.6051-2.9957-0.1278-1.8971-1.9661-2.6592]$

$\chi ^2_0=-2[-22.732]$

$\chi ^2_0=45.464$

So,the test statistics value is $\chi ^2_0=45.464$

The test statistics value exceeds the critical value.Reject the null hypothesis .At 5% level it can be concluded that all P-values are independent