A government worker claims that the standard deviation of the mean weight of all US Postal Service shipments is 0.40 pounds. If a hypothesis test is performed, how should you interpret a decision that
(a) rejects the null hypothesis?
(b) fails to reject the null hypothesis?
First we figure out what the hypotheses are here by this easy trick.
The claim is that the standard deviation (sigma) is equal to 0.40 pounds. Since it includes an "=" sign, it is the null hypothesis "H_0 : sigma = 0.40". Thus, the alternative hypothesis is "H_1: sigma not= 0.40".
Then, depending on which scenario we find ourselves in after testing the hypothesis, we make a decision...
(a) A decision that rejects the null hypothesis says that there is sufficient evidence to support the claim that "H_1 : sigma not= 0.40". (The evidence supports the alternative hypothesis)
(b) A decision that fails to reject the null says that there is not enough evidence to support the claim that "H_1: sigma not= 0.40".