Answer :
We can reject the null hypothesis at the 0.05 level and accept the alternative hypothesis.
A one-sided test will test using the full alpha to test whether the result is far enough in one direction. A two-sided test will split the alpha in half to test whether the result is too big or too small.
The null hypothesis is:
[tex]\mathit{H}_{0}: \mu= 2.5[/tex]
The alternative hypothesis is:
[tex]\mathit{H}_{1}: \mu > 2.5[/tex]
The z-score for a mean of 3 is:
[tex]z = (x- \mu)/ (\sigma/ \sqrt{n})) \\ = (3-2.5)/(1.8/\sqrt{n})) \\ = (.5)/(1.8/6)) \\ = (.5)/(.3)) \\ = 1.666666667[/tex]
The z-score for the 0.05 significance level is 1.645, which is less than the mean of 3 z score of 1.67.
Hence, we can go ahead and reject the null hypothesis
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