2. What is the difference between Type I and Type II error? How does reducing th

Question

2. What is the difference between Type I and Type II error? How does reducing the likelihood of committing one affect the likelihood of committing the other when the rejection level is adjusted either up or down from.05? (3 pts) 3. Create a the null form of a statement (null hypothesis) for a directional hypothesis about the relationship between the variables age and political party preference? (1 pt) 4. Does a statistically significant relationship between variables mean that there is no possibility that the variables are unrelated? Explain. (2 pts) 5. Which rejection level, .01 and.10, suggests a greater likelihood of a true relationship between variables? Explain. (2 pts)

Explanation / Answer

2.

Type I error is the chance of rejecting the true sample. That is we reject the null hypothesis when its actually is true at a given level of significance. The alpha is the significance level which is the probability of committing the type I error. In the area of distribution curve the points falling in the 5% area are rejected , thus greater the rejection area the greater are the chances that points will fall out of a population in this rejection area and thus more probability of incorrectly identifying true samples in the rejection area.If level of significance reduces from 5 to 1% then the rejection area also reduces thus lower rejection area reduces the chances that points will fall out of a population in this rejection area and thus less the probability of incorrectly identifying true samples in the rejection area. Thus the chances of committing the type I error decreases with reduction in the significance level alpha.

So if we lower the significance level from 5% to 1%, is to decide for a 1% probability of Type I error; and the price is a higher probability of a Type II error and vice versa.

3.

If we are testing to see if there is a correlation between age and party preference we might say the older the voter the more (or less) likely it is they will favor party X.

A directional null hypothesis would pick one of these directions:

H0 might be "the older the voter they are not more likely to pick party X"

4.

Statistical significance means that there is a good chance that we are right in finding that a relationship exists between two variables. But statistical significance is not the same as practical significance. We can have a statistically significant finding, but the implications of that finding may have no practical application. The researcher must always examine both the statistical and the practical significance of any research finding.

    For example, we may find that there is a statistically significant relationship between a citizen's age and satisfaction with city recreation services. It may be that older citizens are 5% less satisfied than younger citizens with city recreation services. But is 5% a large enough difference to be concerned about?

    Often times, when differences are small but statistically significant, it is due to a very large sample size; in a sample of a smaller size, the differences would not be enough to be statistically significant.

5. The significance level of 0.01, suggest a greater likelihood of a true relationship between variables.

In general, for every hypothesis test that we conduct, we'll want to do the following:

(1) Minimize the probability of committing a Type I error. That, is minimize = P(Type I Error). Typically, a significance level of 0.10 is desired.

(2) Maximize the power (at a value of the parameter under the alternative hypothesis that is scientifically meaningful). Typically, we desire power to be 0.80 or greater. Alternatively, we could minimize = P(Type II Error), aiming for a type II error rate of 0.20 or less.

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