In: Statistics and Probability
1. In your own words, how is a null hypothesis, different from a
research hypothesis?
2. A statistician is faced with increasing the chances that she
will make a Type I error or increasing the chances that she will
make a Type II error. What advice do you give to her? Why?
3. Discuss how the terms “level of significance” and “critical region” are related.
4. Why would a researcher test a one-tailed vs. a two-tailed hypothesis?
5. Why would it be impossible for a researcher to test the following hypothesis using a t-test? H1: Female homicide offenders are more likely to be sentenced to maximum security prison than male homicide offenders.
6. If the null hypothesis in a t-test for two samples is not rejected, what conclusion can be drawn about the two means of the categorical variable?
7. Two groups of subjects participated in an experiment designed to test the effect of frustration on aggression. The experimental group of 40 subjects received a frustrating puzzle to solve, while the control group of 70 subjects received a very easy version of the same puzzle. Levels of aggression was measured for both groups where higher scores are indicative of higher levels of aggression. The experimental group (high frustration) had a mean aggression score of 4.0 and a standard deviation of 2.0. The control group (no frustration) had a mean aggression score of 3.0 and a standard deviation of 1.5. Using these results, formulate a research and null hypothesis and test the null hypothesis at the .01 level of significance.
8. Assume you collected larger samples of individuals to test
your null hypothesis in question #6. Specifically, the sample sizes
increased to 200 subjects in each group. Do your results and
conclusions change from the test of the smaller sample sizes? (You
must show your work).
1)
A research hypothesis is a specific, clear, and testable proposition or predictive statement about the possible outcome of a scientific research study based on a particular property of a population, such as presumed differences between groups on a particular variable or relationships between variables. Specifying the research hypotheses is one of the most important steps in planning a scientific quantitative research study. A quantitative researcher usually states an a priori expectation about the results of the study in one or more research hypotheses before conducting the study, because the design of the research study and the planned research design often is determined by the stated hypotheses. Thus, one of the advantages of stating a research hypothesis is that it requires the researcher to fully think .
null hypothesis :
The null hypothesis, H0 is the commonly accepted fact; it is the opposite of the alternate hypothesis. Researchers work to reject, nullify or disprove the null hypothesis. Researchers come up with an alternate hypothesis, one that they think explains a phenomenon, and then work to reject the null hypothesis.
Keeping in mind the potential losses due to the wrong decision, the decision maker is somewhat conservative in holding the null hypothesis as true unless there is strong evidence that it is false and to him the consequences of wrongly rejecting a null hypothesis semms to be more serious than those of wrongly accepting it. Hence we denote by H0 that hypothesis among H1 and H2 whose false rejection is regarded as more serious and call it null hypothesis.
3) LEVEL OF SIFNIFICANCE AND CRITICAL REGION.
A critical region W, also known as the rejection region, is a set of values for the test statistic for which the null hypothesis is rejected. i.e. if the observed test statistic is in the critical region then we reject the null hypothesis and accept the alternative hypothesis.
The usual procedure of finding a test of H0 against H1 is to restrict that error probability which is more serious, that is the probability of Type I error and then to minimize the probability of Type II error. Thus one selects a number 0<α<1 and impose condition on critical region W such that P[X ϵ W | Ɵ ] <= α , Ɵ ϵ the parameter space specified by the null hypothesis. Then the quantity α is called the Level of significance of the testing problem.