STATS

• Null hypothesis


  The hypothesis that is assumed to be true. It uses a relation symbol with a statement of equality, such as = and ≤, and is denoted by H0.
• Alternative hypothesis


  The hypothesis that is contrary to the null hypothesis. It uses a relation symbol with no statement of equality, such as ≠ and >, and is denoted by Ha.
• Level of significance


  The probability of rejecting the null hypothesis in favor of the alternative hypothesis when it is really true, denoted by α.
• Rejection region

  The set of values in which the null hypothesis is rejected.
• Steps in Hypothesis Testing

  1. Formulate the null and alternative hypotheses

  2. Determine the level of significance

  3. Calculate the test statistic and identify the rejection region

  4. Make a decision

  5. Draw a conclusion
• Statistical hypothesis


  A statement about a population parameter
• Null hypothesis


  • Uses a relation symbol with a statement of equality, such as = and ≤, and is denoted by H0
• Alternative hypothesis


  • Uses a relation symbol with no statement of equality, such as ≠ and >, and is denoted by Ha
• Directional test of hypothesis or one-tailed test


  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.
• Right-tailed test

  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. The alternative hypothesis uses comparatives such as greater than, higher than, better than, superior to, exceeds, above, increased, etc.
• Right-tailed test


  • The mean number of hours students spend studying after school is greater than 2.5 hours.
• Left-tailed test


  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. The alternative hypothesis uses comparatives such as less than, smaller than, inferior to, lower than, below, decreased, etc.
• Left-tailed test

  • The mean number of hours students spend studying after school is less than 2.5 hours.
• Non-directional test of hypothesis or two-tailed test


  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. The alternative hypothesis uses comparatives such as not equal to, different from, not the same as, etc.
• Non-directional test of hypothesis or two-tailed test


  • The mean number of hours students spend studying after school is not 2.5 hours.
• Null hypothesis


  • There is no difference in the salary of factory workers based on gender.
• Alternative hypothesis


  • Male factory workers have a higher salary than female factory workers.
• Null hypothesis


  • There is no relationship between height and shoe size.
• Alternative hypothesis


  • There is a positive relationship between height and shoe size.
• Null hypothesis


  • Experience on the job has no impact on the quality of a brick mason's work.
• Alternative hypothesis


  • The quality of a brick mason's work is influenced by on-the-job experience.
• Null hypothesis


  • The daily mean number of customers in the clothing shop is less than or equal to 246.
• Alternative hypothesis


  • The daily mean number of customers in the clothing shop is greater than 246.
• Hypothesis testing is a statistical method of using sample data to determine the probability that a given hypothesis about the population is true.</b>
• The steps in hypothesis testing are: Formulate the null and alternative hypotheses, Determine the level of significance, Calculate the test statistic and identify the rejection region, Make a decision, Draw a conclusion.</b>
• A statistical hypothesis is a statement about a population parameter.
• The null hypothesis is the hypothesis that is assumed to be true.
• The alternative hypothesis is the hypothesis that is contrary to the null hypothesis.
• 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.
• A 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.
• 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.
• A 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.
• The level of significance is the probability of rejecting the null hypothesis in favor of the alternative hypothesis when it is really true.
• The rejection region is the set of values in which the null hypothesis is rejected.
• Berman, Harvey: '"What is Hypothesis Testing?" Stat Trek.'
• Glen, Stephanie: '"Hypothesis Testing." Statistics How To.'
• Type I error


  An error in hypothesis testing that occurs when a true null hypothesis is rejected
• Type II error


  An error in hypothesis testing that occurs when a false null hypothesis is not rejected
• Preclinical testing and clinical trials are required in medicine before a drug may be approved for use on the market
• Pharmaceutical corporations conduct tests before a future medicine is ever administered to a human being