Statistical Inference Testing of Hypothesis

  • Type 1 Error and Type 2 Error

    The null hypothesis is accepted or rejected on the basis of the value of the test-statistic which is a function of the sample. The test statistic may land in acceptance region or rejection region. If the calculated value of test-statistic, say , is small (insignificant) i.e., is close to zero or we can say lies […]

  • Two Tailed Test

    When the rejection region is taken on both ends of the sampling distribution, the test is called two-sided test or two-tailed test. When we are using a two-sided test, half of the rejection region equal to is taken on the right side and the other half equal to is taken on the left side of […]

  • One Tailed Test

    When the alternative hypothesis is one-sided like or , then the rejection region is taken only on one side of the sampling distribution. It is called one-tailed test or one-sided test. When is one-sided to the right like, the entire rejection region equal to is taken in the right end of the sampling distribution. The […]

  • Acceptance and Rejection Regions

    All possible values which a test-statistic may assume can be divided into two mutually exclusive groups: one group consisting of values which appear to be consistent with the null hypothesis and the other having values which are unlikely to occur if is true. The first group is called the acceptance region and the second set […]

  • Test Statistic

    A statistic is calculated from the sample. To begin with we assume that the hypothesis about the population parameter is true. We compare the value of the statistic with the hypothetical value of the parameter. If the difference between them is small, the hypothesis is accepted and if the difference between them is large, the […]

  • Simple Hypothesis and Composite Hypothesis

    A simple hypothesis is one in which all parameters of the distribution are specified. For example, if the heights of college students are normally distributed with , the hypothesis that its mean is, say,, that is , we have stated a simple hypothesis, as the mean and variance together specify a normal distribution completely. A […]

  • Accept and Reject Null Hypothesis

    The given hypothesis is tested with the help of the sample data. A simple random sample has the full freedom of giving any value to its statistic. The sample is not aware of our plans. We decide about our hypothesis on the basis of the sample statistic. If the sample does not support the null […]

  • Alternative Hypothesis

    The hypothesis which is accepted when the null hypothesis has been rejected is called the alternative hypothesis. It is denoted by or . Whatever we are expecting from the sample data is taken as the alternate hypothesis. “More than 25% people are literate in our country”. We are hoping to get this result from the […]

  • Null Hypothesis

    The hypothesis which is to be tested is called null hypothesis.It is denoted by . It is a starting point in the investigations. A statement which we hope will be rejected is taken as a hypothesis. Modern approach is different. Today any hypothesis we wish to test is called null hypothesis and is denoted by […]

  • Statistical Hypothesis

    Any opinion or idea may be formed about the population under study. Consider the following statements: Average consumption of sugar per month for a consumer is 1 kg; Intelligent parents have intelligent children, tall fathers have tall sons, average life of the people of Pakistan is higher than that of India, proper greasing increases the […]

  • Statistical Inference

    Statistical inference consists of estimation of parameters and testing of hypotheses. Estimation has already been discussed this content is about the testing of hypotheses. Point estimation and interval estimation as discussed earlier have their own fields of application. Sometimes there is a situation in which the point estimation and the interval estimation are either not […]