Hypothesis test involves the process of making a choice between possible statements relating to a population. The possible values of the population are denoted by ρ and after some adjustment while testing the hypothesis the possible values of the population mean are indicated as µ. For the null hypothesis have an equality which lacks in the alternative hypothesis.
| Research Question | Is the proportion different from µ 0 ? | Is the proportion greater than µ 0 ? | Is the proportion less than µ 0 ? |
| Null Hypothesis, H0 | µ = µ 0 | µ = µ 0 | µ = µ 0 |
| Alternative Hypothesis, Ha | µ ≠ µ 0 | µ > µ 0 | µ < µ 0 |
| Type of Hypothesis Test | Two-tailed, non-directional | Right-tailed, directional | Left-tailed, directional |
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The hypothesized value of the population proportion is µ 0. In this case, it is through examining the mean value that quantitative variables are summarized. The categorical variables are summarized based on each category’s proportion.
A mean in Null and Alternative Hypothesis
The typical null hypothesis is H0 for a single population mean while the population mean µ= a specified values. Where there is a special value, a number is used while the null hypothesis of paired indicated as H0: U d = a specified value. However, the specified value is equal to zero when considering the variances. On the other hand, the alternative hypothesis may be considered to be one-sided or two-sided. If it is one-sided, there will be a specific direction of inequality while two-sided there is a not equal statement.
Statistics testing for one population mean
Where: represent the observed sample mean
μ 0 represents null hypothesis specified value
S is the standard deviation of the sample measurement, and lastly, n represents the number of differences.
Statistic test for paired data will be equal to:
References
Johnson, V. E. (2013). Revised standards for statistical evidence. Proceedings of the National Academy of Sciences , 110 (48), 19313-19317.
Nathoo, F. S., & Masson, M. E. (2016). Bayesian alternatives to null-hypothesis significance testing for repeated-measures designs. Journal of Mathematical Psychology , 72 , 144-157.
