Indicate the null H0 and alternative hypothesis Ha you would

Indicate the null (H0) and alternative hypothesis (Ha) you would develop for the following problems (you do not have to solve the problem)

a) 5% of trucks of a certain model have needed new engines after being driven between 0 and 90 miles. The manufacturer hopes that the redesign of one of the engine\'s components has solved this problem.

b) A weight loss center provided a loss for 87% of its participants. The center\'s leader decides to test a new weight loss strategy to see if it\'s better.

Solution

a. This is a one sided problem testing whether the proportion of trucks of a certain model that needed new engines after being driven between 0 and 90 miles has decreased or not.

Null: the proportion of trucks of a certain model that needed new engines after being driven between 0 and 90 miles is 5% after redesigning

Alternate: the proportion of trucks of a certain model that needed new engines after being driven between 0 and 90 miles is less than 5% after redesigning

b. This is a one sided problem testing whether the proportion of participants had a weight loss has increased after a new strategy for weight loss was implemented.

Null: the proportion of participants that had a weight loss after a new strategy for weight loss was implemented is 87%

Alternate: the proportion of participants that had a weight loss after a new strategy for weight loss was implemented is more than 87%