Question

Preliminary data analyses indicate that it is reasonable to use as to carry out the specified hypothesis test. Perform the best using the critical approach Use a cance level of 0.01 to test the claim that > 285 The sample data con of for which 312-05 For the toolbarbe ALT FOCALTANATOM TTTT Prah Al XDOQEEZE TT.

Answer 1

We are testing here whether the population mean is more than 2.85. The test statistic here is computed as:

$t^* = \frac{\bar X - \mu_0}{\frac{s}{\sqrt{n}}} = \frac{3.12 - 2.85}{\frac{0.52}{\sqrt{9}}} = 1.56$

For n - 1 = 8 degrees of freedom, and 0.01 level of significance, we have from t distribution tables here:

P( t₈ < 2.896 ) = 0.99

Therefore P( t₈ > 2.896) = 1 - 0.99 = 0.01

Therefore 2.896 is the required critical value here.

As the test statistic value here is 1.56 < 2.896, therefore it lies in the non rejection region here. Therefore we cannot reject the null hypothesis here. We have insufficient evidence that the mean is more than 2.85 here.