Choosing the correct hypotheses I was trying out some questions on hypothesis testing when some questions started challenging me. Here is an example:
A lot of product X is to be rejected if the temperature of the lot is greater than $75$ degree Celsius and is to be expected if the case is otherwise? (Then the question gives some data regarding a sample and asks) Should the lot be rejected?
What should be by alternate hypothesis in the question. How would I know what the researcher wants to prove through his research?
One more question on the same lines:
A company will open a new store in the area if more than $5 \%$ of the people of the area had good opinion about its products. (Then some data is given regarding a sample that we collected and asks) Should the company open store in the area?
Kindly tell me the thought procedure involved in the process of choosing null and alternate hypotheses.
 A: It sounds like the difference is only interesting to you if the difference is in a particular direction, so one-sided testing would be appropriate. If you did two-sided testing, I'm imagining this conversation with your boss.
YOU: "...and then after hypothesis testing, I conclude that it was not 75 degrees celcius, and 5% of people did not have a positive opinion of the products. I rock!"
BOSS: "Was it hotter or colder than 75 degrees?"
YOU: "I didn't test that, just if it's 75 degrees."
BOSS: "Did fewer or more than 5% of people have a positive opinion?"
YOU: "I didn't test that, just if it's 5%."
BOSS: "How enlightening..."
If you do one-sided testing, you can answer her questions.
For the first situation:
$$H_0: \theta \le 75 ^\circ C$$
$$H_a: \theta > 75 ^\circ C$$
For the second situation:
$$H_0: \theta \le 5\%$$
$$H_a: \theta > 5\% $$
In both cases, $\theta$ is whatever it is that you're measuring. It's a common variable to use in statistics, and it doesn't necessarily have anything to do with angles like you may be thinking from trig or physics class.
NOTE: Many teahers, particularly in intro classes, will write the following:
$$H_0: \theta = 5\% $$
$$H_a: \theta > 5\% $$
This is equivalent to what I wrote above.
