In comparing the means of two samples that are considered random in order to test whether a significant difference exists, one would use the t test method of hypothesis testing.
Yes, you are correct. The t-test is commonly used to compare the means of two independent samples in order to determine if there is a significant difference between them. The hypothesis testing process typically involves the following steps:
1. State the null hypothesis (H0) and the alternative hypothesis (Ha): In this case, the null hypothesis states that there is no significant difference between the means of the two samples, while the alternative hypothesis states that there is a significant difference.
2. Choose the significance level (α): The significance level is the probability that we are willing to accept as the threshold for rejecting the null hypothesis. Common values for α are 0.05 (5%) or 0.01 (1%).
3. Calculate the test statistic: In the case of comparing two sample means, the test statistic is the t-value. The formula for the t-value depends on whether the samples are assumed to have equal or unequal variances.
4. Determine the critical region: The critical region is the range of values that, if the test statistic falls within it, would lead to rejecting the null hypothesis. The critical values for the t-distribution are based on the degrees of freedom (df), which is determined by the sample sizes and assumptions about variance equality.
5. Compare the test statistic with the critical values: If the test statistic falls within the critical region, we reject the null hypothesis. If it falls outside the critical region, we fail to reject the null hypothesis.
6. Calculate the p-value (optional): The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. If the p-value is smaller than the specified significance level, we reject the null hypothesis.
Overall, the t-test is a powerful tool for comparing means and determining if a significant difference exists between two independent samples.