Question

Directions: Answer the following question in 1-2 double-spaced pages. Please be detailed and thorough.

In words your 12-year old cousin would understand, what does it mean to test a hypothesis? In formulating your response, you should think through (and describe) the logic of hypothesis testing as well as the significance of each step you follow when per-forming such a test. Your answer should include a discussion on the null and alternative hypotheses, the logic of testing a null hypothesis (that is, explain what exactly you’re doing when you plug the numbers into the formula for a z-score or t-test – what are youtrying to find?), establishing criteria that lead you to “reject” or “fail to reject” the null, and how one uses all of this information to reach a conclusion.

Answer 1

In general we want to check the calim about population parameters like mean,proportion etc but generally populations are very large and so we take a sample from the population then we observe and analyze the sample and depends on sample observations we test the claim about the population this process is know as hypothesis testing.

Hypothesis testing have to hypothesis

1.null hypothesis:its general claim about population like mean=20 or meam<21 of a population etc.we can define it's a hypothesis of no difference between population parameter and sample observations.

2.alternative hypothesis: hypothesis made apposite to null hypothesis is known as alternative hypothesis like mean not equal to 20 or mean_>21 etc

Next step is to calculate statistics

When we testing the mean

Then

Calculate the sample mean=m

Sample size=n

Sample observed Standard deviation=S

For n<30

Then t is T distribution with df=n-1

If the n>30 then its Z distribution

While if population standard deviation is given then use Z statistics

Then find the P value

P value=P(finding observed or more extreme result assuming null is true)

When P value <given level of signicance

Then we reject the null hypothesis

Otherwise fail to reject the null hypothesis