Zander - Stat and Prob

• Hypothesis testing - is a statistical method of using sample data to determine the probability that a given hypothesis about the population is true.
• statistical hypothesis - is a statement about a population parameter.
• The hypothesis that is assumed to be true is called a null hypothesis. It uses a relation symbol with a statement of equality, such as ≥,  ≤, and =, and is denoted by H_0.
• The hypothesis that is contrary to the null hypothesis is called the alternative hypothesis. It uses a relation symbol with no statement of equality, such as >, <, and ≠, and is denoted by H_A.
• A directional test of hypothesis or one-tailed test is a type of hypothesis test that uses only one side or tail of the distribution. It can either be a right-tailed or left-tailed test.
• The right-tailed test is a type of directional test of hypothesis or one-tailed test used when it is hypothesized that the parameter falls within the positive end of the distribution. In a right-tailed test, the alternative hypothesis uses comparatives such as greater than, higher than, better than, superior to, exceeds, above, increased, etc.
• A left-tailed test is a type of directional test of hypothesis or one-tailed test used when it is hypothesized that the parameter falls within the negative end of the distribution. In a left-tailed test, the alternative hypothesis uses comparatives such as less than, smaller than, inferior to, lower than, below, decreased, etc.
• Non-directional test of hypothesis or two-tailed test is a type of hypothesis test that uses two opposite sides or tails of the distribution. It is used when no assertion is made on whether the parameter falls within the positive or negative end of the distribution. In a two-tailed test, the alternative hypothesis uses comparatives such as not equal to, different from, not the same as, etc.
• The level of significance is the probability of rejecting the null hypothesis in favor of the alternative hypothesis when it is really true, denoted by α.
• The rejection region is the set of values in which the null hypothesis is rejected.
• the parameter refers to the characteristic or measure of a population. This is also referred to as the true or actual value.
• Parameters refers to the characteristic or measure of a population.
• Hypothesis testing is the process of making inference and decision based on a given data through statistical tests.
• the rejection region or critical region is the set of all values of the test statistic that causes us to reject the null hypothesis.
• population standard deviation is a parameter which is a measure of variability with fixed value calculated from every individual in the population.
• a test statistic is a random variable that is acalculated from sample data and used in a hypothesis test.
• the numerical measure that is a calculated from the sample is called statistic.
• the critical value is a point on the test distribution that is compared to the test statistic to determine if the null hypothesis would be rejected.
• Correct decision - true and she fails to reject
• type 1 error - true and she rejects it
• type 2 error - false and she fails to reject it
• correct decision - false and she rejects it
• Answer V1.