Hypothesis Testing Procedures in Inferential Statistics

The two major types of statistical inference are hypothesis testing and confidential intervals. We use these two methods to make inferences. The difference between the use of the confidence intervals and hypothesis testing in inferential statistics is that the two have different goals. In hypothesis testing, we make some claim about a population based on the analysis of the evidence provided by our data. Where as in latter, an estimate of a population parameter is made. ¹

The concepts of the p-value and confidence intervals are related as measures of statistical significance in the sense that both confidence intervals and p values use probability to try to answer research questions using samples of a population. They can both help you decide whether to deny or accept a null hypothesis. They are both an approach to estimation and lastly, you can use confidence intervals or p values with most of the statistical tests.²

Writing a null and alternative hypothesis using 5- step approach to hypothesis testing

In an example of hypothesis testing using step 5 – step approach to hypothesis testing, I conduct an investigation whether the IQ’s of RMIT Scholars are higher than the overall Australian population. ³

Random sample = 37 students.

Students’ IQ mean = 106.

The fact is that IQ = normal distribution. Mean (mµ) = 100. Sigma = 15.

1. State hypothesis (NULL and ALTERNATIVE)

Null hypothesis = presumed value of parameter (H₀) – statistical hypothesis that we test (strength of our sample data vs. the null hypothesis).

H₀ : µ = 100

Alternative hypothesis = contingent value if null rejected (H₁) – statement that specifies what we think is true (usually the opposite of the null hypothesis).

H₀ : µ ≠ 100 OR H₀ : µ > 100 OR H₀ : µ < 100. ⁴

2. State significance level (Level of rejecting a TRUE hypothesis)

The Z Statistic – n >30

Z = 2.76

3. Select test distribution to use

α = probability of denouncing (e.g., 2%)

1 – α = probability un-rejected (e.g. 99%) } ** Test distribution to be used**

4. Define area of rejection

I find the P- value. Z – score = 2.75. The probability of this result from the sample data set =.0029. I am using the 1 – tailed test (> direction), therefore use the second half of the distribution ⁵.

i.e. P-value ; 1-.9971 =.0029

A-crit for alpha.05 = 1.64

The observation from the data result suggests that it’s highly unlikely that the hypothesis is true. Therefore we have rejected the hypothesis.

Also from the result of conducted calculation, the Z-score i.e. 2.76 is > the Z-crit i.e. 1.64, is another reason to reject the null hypothesis. ⁶

5. State decision rule (Conclusion)

RMITs students’ IQ is generally higher than the overall Australian population at the.05 level. I therefore have rejected the null hypothesis.

The Chi-Square goodness of is calculated using the below formula

References

Confidence intervals & hypothesis testing (1 of 5). (n.d.). HyperStat Online. Web.

Counts, t. s., & below:, a. s. (n.d.). Yale Statistics website. Web.

Population., o. d. (n.d.). HTCIP: Yale University. Web.

Preacher, K. J. (n.d.). Interactive Chi-square tests. Kristopher J. Preacher. Web.

What Is the relationship between confidence intervals and hypothesis testing. (n.d.). FTPRPEBROPP.com. Web.

Footnotes

1. Population., o. d. (n.d.). HTCIP: Yale University. Web.
2. Confidence intervals & hypothesis testing (1 of 5). (n.d.). HyperStat Online. Web.
3. population., o. d. (n.d.). HTCIP:. Yale University. Web.
4. Preacher, K. J. (n.d.). Interactive Chi-square tests. Kristopher J. Preacher. Web.
5. Counts, t. s., & below:, a. s. (n.d.). Yale Statistics website. Web.
6. What Is the relationship between confidence intervals and hypothesis testing. (n.d.). FTPRPEBROPP.com. Web.
7. Preacher, K. J. (n.d.). Interactive Chi-square tests. Kristopher J. Preacher. Web.