When comparing two samples that are independent of one another, we use the two-sample t-test.
A) True
B) False
5.
Using paired differences helps to reduce the variation.
A) True
B) False
Both are True?
Yes, both are true.
To answer these questions, we'll need to understand the concepts and steps involved in performing a two-sample t-test and using paired differences.
1. Two-sample t-test: A two-sample t-test is used to compare the means of two independent samples. The test assesses whether the means are significantly different from each other. To perform a two-sample t-test, follow these steps:
a. Formulate the null hypothesis (H0) and alternative hypothesis (H1) based on what you want to test.
b. Collect data from the two independent samples.
c. Calculate the means of each sample.
d. Calculate the standard deviations of each sample.
e. Calculate the t-value using the formula: t = (mean1 - mean2) / √( (s1^2/n1) + (s2^2/n2)), where mean1 and mean2 are the means, s1 and s2 are the standard deviations, and n1 and n2 are the sample sizes.
f. Compare the calculated t-value with the critical t-value from the t-distribution table, considering the degrees of freedom.
g. Determine the p-value associated with the calculated t-value using a t-distribution table or statistical software.
h. Make a decision based on the p-value and the predetermined significance level (alpha). If the p-value is less than alpha (typically 0.05), reject the null hypothesis. If the p-value is greater than or equal to alpha, fail to reject the null hypothesis.
Based on the steps above, the statement "When comparing two samples that are independent of one another, we use the two-sample t-test" is True (option A).
2. Paired differences: Paired differences refer to the idea of comparing two variables that are measured on the same subjects. Paired differences are typically useful when there is a natural pairing between measurements or when comparing pre- and post-measurements for the same individuals. The paired differences can help reduce variability by eliminating the influence of individual characteristics. To use paired differences in statistical analysis, you can follow these steps:
a. Identify the paired variables.
b. Calculate the difference between the paired measurements for each individual.
c. Analyze the resulting differences as a separate dataset.
d. Perform statistical tests or analysis on the paired differences.
Based on these steps, the statement "Using paired differences helps to reduce the variation" is also True (option A).
Therefore, your answer is correct. Both statements are True.