Statistics

statistics

#1

Can the formal hypothesis testing approach be used for nonparametric tests?

Yes, the approach is identical to the one used for parametric tests.

How are parametric and nonparametric statistics different?

Behind parametric statistics there are very specific assumptions about the nature of the PDF that the data presumably represent.

A way of dealing with the additional uncertainty introduced by violated assumptions is to use Non-parametric test statistics whose PDF’s remain the same, regardless of how the population sampled may change.

How are parametric and nonparametric statistics similar?

There is at least one nonparametric test equivalent to a parametric test. Just as among the parametric tests we need to know when to use a certain nonparametric test.

#2

Under what circumstances should a nonparametric test be used? Explain.

In situations when less is known about the population in question. Nonparametric statistics can for example be necessary when data has a ranking but no clear numerical interpretation (customer satisfaction).

What are the strengths and weaknesses of nonparametric tests?

Strengths: less assumptions / greater robustness

Weaknesses: Low power / wasteful of data

Can the outcomes of nonparametric tests be generalized to populations?

Yes

#3

Why do you use the chi-square statistic?

Test (draw conclusions about) variances.

Test if a sample of data came from a population with a specific distribution.

Test of independence.

What type of data is used with chi square analysis?

When testing variances the data is continuous and assumed to come from a normal distribution. The goodness of fit test handles only discrete data (but we can still use continuous data by dividing it to discrete data). The test of independence handles categorical data.

#4

a)

H0: p1 = p2

Ha: p1 > p2

b)

Reject H0 if z > 2.326

[pic]

c)

[pic]

[pic]

d)

Since the test statistic is in the rejection region, we...