Homework SourseConsider the following competing hypotheses and accompanying
Consider the following competing hypotheses and accompanying sample data. Use Table 1.
Calculate the value of the test statistic. (Negative values should be indicated by a minus sign.Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
At the 10% significance level, calculate the critical value. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)
| Consider the following competing hypotheses and accompanying sample data. Use Table 1. |
| H0: p1 ? p2 ? 0 |
| HA: p1 ? p2 < 0 |
Solution
(a) p1=224/442=0.5067873
p2=236/442 = 0.5339367
The test statistic is
Z=(p1-p2)/sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)
=(0.5067873-0.5339367)/sqrt(0.5067873*(1-0.5067873)/442+0.5339367*(1-0.5339367)/442)
=-0.81
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(b) It is a left-tailed test.
Given a=0.1, the critical value is Z(0.1) =-1.282 (from stnadard normal table)
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(c)Do not reject H0 since the value of the test statistic is not less than the critical value.
