Summary
Interval estimators specify methods of measuring sample that can be used to determine endpoint values of an interval. Intervals have a target parameter, and they are relatively narrow. At least one endpoint varies randomly since they are sample measurement functions. Interval estimators are confidence intervals with lower and upper limits. Confidence coefficient is the probability of intervals having a target parameter.
Hypothesis testing is a procedure of using observations to test theories. Theories concerning population parameters are sampled and compared with observations. If observations do not match with the theory, the hypothesis is rejected as false, otherwise the theory is true. Hypothesis testing is done in many fields such as teaching and engineering among others. Statistics have a significant role in hypothesis testing. Statistical tests are meant to test hypotheses about a single population or several populations. A hypothesis can have supporting theories called alternative hypothesis, whose converse is a null hypothesis. If the statistical evidence is in favor of the alternative hypothesis, the null hypothesis is rejected at the expense of the alternative hypothesis .
For example, if the alternative hypothesis is, the probability of picking a voter who supports Jones is not more than 0.5. This will be presented as p<0.5 while p=0.5 is the rejection point. To decide between a null and alternative hypothesis using data, the following procedure is followed. Statistical data is used to determine which hypothesis is correct. If n=15 voters are picked randomly from the population and it if found that Y people favor Jones. If no one in that sample supports Jones, y=0. It is possible for Jones to have 0 supporters in a sample of 15 though that probability is very low. If the alternative hypothesis is true, p=0.5, it is likely to see y=0, which will lead to the rejection of the null hypothesis of p=0.5. Statistical tests of all hypotheses are similar in that they are composed of; a test statistic, null hypothesis (Ho), alternative hypothesis (Ha), and a rejection region. In the example, the null hypothesis is p=0.5 while the alternative hypothesis is the one being sought to be approved or disapproved. The alternative hypothesis is p<0.5. A statistical test is composed of the rejection region and the test statistic. A test statistic is a sample measurement function on which the statistical decision is based. The rejection area is denoted by RR and it gives the test statistic values that determine whether to accept or reject the null hypothesis. In any sample, a test statistic falling in the rejection area, accept the alternative hypothesis and reject the null.
Works Cited
Harmon, Mark. Hypothesis Testing in Excel - The Excel Statistical Master. New York: Mark Harmon, 2011.
Poletiek, Fenna. Hypothesis-Testing Behaviour. illustrated. New York: Psychology Press, 2001.
Siegmund, David. Sequential Analysis: Tests and Confidence Intervals. Munich: Springer, 1985.
Smithson, Michael. Confidence intervals, Issue 140. 2, illustrated. New York: Sage Publications, 2003.
Tiku, Moti Lal and Ayşen D Akkaya. Robust Estimation And Hypothesis Testing. New York: New Age International, 2004.
