A significance test was performed to test the null hypothesis \( H_0: \mu = 2 \). This test is crucial in statistical analysis as it helps researchers determine whether the observed data is consistent with the null hypothesis or if there is sufficient evidence to reject it. The significance test is an essential tool in hypothesis testing, allowing for the evaluation of the likelihood that the observed data could have occurred by chance.
In this particular study, the null hypothesis \( H_0: \mu = 2 \) assumes that the population mean is equal to 2. The alternative hypothesis \( H_1: \mu eq 2 \) suggests that the population mean is not equal to 2. To test these hypotheses, a sample of data was collected and analyzed using a suitable statistical test.
The chosen statistical test for this significance test was the t-test, which is commonly used when the population standard deviation is unknown and the sample size is small. The t-test compares the mean of the sample to the hypothesized population mean and calculates a p-value to determine the strength of the evidence against the null hypothesis.
The t-test was conducted using the following steps:
1. Calculate the sample mean (\(\bar{x}\)) and sample standard deviation (s).
2. Calculate the test statistic (t-value) using the formula: \( t = \frac{\bar{x} – \mu}{s/\sqrt{n}} \), where \(\mu\) is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
3. Determine the degrees of freedom (df) for the t-distribution, which is calculated as \( df = n – 1 \).
4. Use the t-distribution table or statistical software to find the p-value associated with the t-value and df.
5. Compare the p-value to the chosen significance level (alpha) to make a decision regarding the null hypothesis.
The results of the significance test revealed a p-value of 0.045. Since the p-value is less than the chosen significance level of 0.05, we reject the null hypothesis. This suggests that there is sufficient evidence to conclude that the population mean is not equal to 2.
This finding is significant for the study as it indicates that the observed data is not consistent with the null hypothesis. Further investigation may be required to determine the actual population mean and identify the factors contributing to the deviation from the hypothesized value. The significance test has provided valuable insights into the data and has helped to guide the research in this direction.
In conclusion, a significance test was performed to test the null hypothesis \( H_0: \mu = 2 \). The results of the t-test indicated that the population mean is not equal to 2, suggesting that the observed data is not consistent with the null hypothesis. This finding has important implications for the study and provides a foundation for further research.
