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Jul
Fail To Reject The Null Hypothesis. Failing to reject the null hypothesis does not mean that the null hypothesis is true. Fail to reject the null hypothesis there is sufficient evidence that the mean REM sleep time for children is more than for adults. Disprove a null hypothesiS does not prove that null hypothesis. Therefore if the value we get for Z from the test is lower than minus 196 or higher than 196 we will reject the null hypothesis.
E Interpret your conclusion in the context of the application. The greater accuracy of the latter interpretation far out weighs the fact that it is a more cumbersome phrase. Fail to Reject the Null Hypothesis is a confusing triple negative. Alternatively if the significance level is above the cut-off value we fail to reject the null hypothesis and cannot accept the alternative hypothesis. After you perform a hypothesis test there are only two possible outcomes. This means that if the P value is less than 005 you reject the null hypothesis.
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The data favors the alternative hypothesis. Disprove a null hypothesiS does not prove that null hypothesis. Fail to reject the null hypothesis there is insufficient evidence that the mean REM sleep time for children is more than for adults. When your p-value is less than or equal to your significance level you reject the null hypothesis. Thats more or less how hypothesis testing works. If the null hypothesis is false then the correct outcome is failing to reject the null.