Question

1. How are efficiency and dispersion related?

2. What are the assumptions to justify the use of hypothesis testing?

3. If the null hypothesis is rejected, what can we conclude? If we know that 60% of ASU students like the parking and 50% of the community as a whole likes the parking, and the difference between the sample and population are tested, with the null rejected, what do we conclude? Is the difference significant? Not significant? Are ASU students significantly more likely or less likely to like the parking? Are they equally likely?

7. In order to reject the null when using a t distribution with small samples, what is needed? Consider size of the test statistic. Why?

Answer 1

1)

Efficiency and dispersion are directly related, the lower the dispersion in the data more the efficient our estimor would be.

Because less dispersion means less variability exist in the data and you can the estimator to be good even if it gives you the more precisive value and when the data has lower variability the chances of error would be reduced.

That's how efficiency and dispersion are related.

2)

Assumptions to justify the use of hypothesis are as followed:

-> It is very difficult thing to answer because hypothesis testing is very much different from the assumption.We take hypothesis testing explicitly whereas assumption would be implicitly, but there could be assumptions lying under the hypothesis.

-> Assumptions under the hypothesis testing vary from test to test. It matters that what kind of research we are going through with and what type of test we will apply to reach our predictive conclusion.

3)

If null hypothesis you have set is rejected then it means that the data you have had is not sufficient for the result you are willing to get. To get to an more accurate and desirable result you need /or require more data.

-> if the null hypothesis gets rejected this means that you got statistically significant result and you need more data to dig in from the community. because 60% sampled data of ASU students is not sufficient.

-> Yes the difference is statistically significant.

-> ASU students are not equally likely to the parking.

7)

To reach the conclusion of rejecting the null hypothesis you need to find the p-value of the distribution.

And according to the decision theory, when the p-value <0.05 we reject the null hypothesis we have set.

In t-distribution size of the statistic matter because to calculate p-value you would require the degree of freedom , which you can find out via sample size.