Statistics. Using T-Test in Hypothesis Testing Coursework

In descriptive statistics, there are always two statistical hypotheses for an experiment. Only one of the two will be supported at the end of the experiment. The other will not be supported. Therefore, for a valid result, the two hypotheses must cover all the possibilities or else the wording of the problem is too complex and must be simplified. The two hypotheses are termed the alternative or experimental hypothesis and the null hypothesis. A non-directional hypothesis should be used since all possibilities are covered if the null hypothesis covers positive possibilities and the opposite is accomplished by adding the word “not” to the null hypothesis. In a directional hypothesis, care must be taken to perfectly match the null hypothesis so that all possibilities will be covered. It is important in testing hypotheses that no other outcome than those allowed for in the statements is possible.

• A non-directional experimental hypothesis might be:
  • H₁: Coffee affects blood pressure
• The corresponding non-directional null hypothesis:
  • H₀: Coffee does not affect blood pressure

( Note: all possible outcomes to the experiment are represented by one of the two hypotheses).

A uni-directional (or non-directional) hypothesis must perfectly match the experimental hypothesis. It is best to create the alternative hypothesis first.

A unidirectional (positive) experimental hypothesis might be:

• H₁: Coffee raises blood pressure.
  • The corresponding null hypothesis would be:
• H₀: Coffee does not raise blood pressure or, equivalently,
• H₀: Coffee raises blood pressure or does not affect blood pressure

Note that a null hypothesis that said: H₀: Coffee lowers blood pressure would not be correct since the possible outcome of coffee not affecting blood pressure is not accounted for in either the experimental or null hypothesis.

• For a unidirectional (negative) experimental hypothesis, an example might be:
  • H₁: Coffee lowers blood pressure
• The corresponding null hypothesis would be:
  • H₀: Coffee does not lower blood pressure

In testing these hypotheses, the z test is used when there is a single sample in the experiment and both the population means and the population standard deviation are known. The one-sample t-test is used when there is a single sample in the experiment and the population means are known, but not the population standard deviation. Therefore, the t-test is more appropriate in research where no control is possible, and in research where the populations cannot be matched because it requires less information than the z-test to be valid.

References

Statistical Power, 2008, C-Engage Learning. Web.

The Research Methods Knowledge Base, 2008, Descriptive Statistics.