given a sample size of 30, and one sample t=-2.5, what would conclude about the sample from which the mean was drawn?
To determine what you can conclude about the sample from which the mean was drawn, you would need to perform a hypothesis test. The hypothesis test compares the observed sample mean to a hypothetical value, assuming a certain population mean.
Here are the steps to perform a hypothesis test in this scenario:
1. State the null hypothesis (H₀): This is the assumption that there is no significant difference between the observed sample mean and the hypothetical population mean. In this case, it would be H₀: μ = μ₀, where μ is the population mean and μ₀ is the hypothetical value.
2. State the alternative hypothesis (H₁): This is the opposite of the null hypothesis and represents the possibility of a significant difference between the observed sample mean and the hypothetical population mean. In this case, it would be H₁: μ ≠ μ₀ (two-tailed test), indicating a difference in either direction from the hypothetical value.
3. Choose the significance level (α): This determines the threshold for rejecting the null hypothesis. Commonly used values are 0.05 or 0.01, indicating a 5% or 1% chance of mistakenly rejecting the null hypothesis.
4. Calculate the test statistic: In this case, you would use the t-test since the population standard deviation is unknown. The formula for the t-test is t = (x̄ - μ₀) / (s/√n), where x̄ is the sample mean, μ₀ is the hypothetical value, s is the sample standard deviation, and n is the sample size.
5. Determine the critical value: This is the value beyond which you reject the null hypothesis. In a two-tailed test, you would split the α level (e.g., 0.05) into two equal tails (e.g., 0.025 in each tail).
6. Compare the test statistic to the critical value: If the test statistic falls outside the critical value range, you reject the null hypothesis and conclude that there is a significant difference between the observed sample mean and the hypothetical population mean. If the test statistic falls within the critical value range, you fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference.
Keep in mind that the above steps provide a general overview of hypothesis testing. The calculation of specific values depends on the distribution of the population or assumptions made about it. It is also recommended to use statistical software or consult with a statistician to perform an accurate hypothesis test.