I do not understand how to find the critical values of the test statistics.
I also need help understanding how to find the standard error as well.
Thank you!
You can find standard error by taking the standard deviation divided by the square root of the sample size.
Critical values determine whether or not to reject the null hypothesis. If you have an observed test statistic (calculated from a formula) that exceeds a critical value from a table, then you have to reject the null hypothesis and accept the alternative hypothesis. If the observed test statistic does not exceed the critical value from a table, then you fail to reject the null hypothesis. For example, how do you translate a significance level of 0.05 into a critical value? It depends on the type of test you are doing. For a one-tailed test, you don't split the value. For a two-tailed test, you split the 0.05 into 0.025 and 0.025 for both tails of the distribution curve (a two-tailed test is like a confidence interval in that respect). If you use a z-table for a one-tailed test at 0.05 level of significance (meaning the alternative hypothesis is showing a specific direction like "less than" or "greater than" in its statement), then you will have a critical value of z = -1.645 or it could be z = 1.645, depending on the direction. This will determine where you "draw the line" to reject the null hypothesis. If you use a z-table for a two-tailed test at 0.05 level of significance (meaning the alternative hypothesis is showing no specific direction and uses "does not equal" in its statement), then you will have a critical value of z = + or - 1.96 (meaning either tail of the distribution curve). For example, if you had a test result of z = +2.00, then you would have exceeded the positive critical value of +1.96 for this particular test result and the null hypothesis would be rejected in favor of the alternative hypothesis.
I hope this will help.
To find the critical values of a test statistic, you typically need to determine the significance level of your hypothesis test and the degrees of freedom for your test statistic. Here's a step-by-step explanation of how to find the critical values:
1. Determine the significance level: The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true. Commonly used significance levels are 0.05 (5%) and 0.01 (1%). It represents how confident you want to be in your decision to reject the null hypothesis.
2. Determine the distribution of the test statistic: The distribution of the test statistic depends on the specific hypothesis test you are performing. For example, if you are conducting a t-test, the test statistic will follow a t-distribution. If you are conducting a z-test (when you know the population standard deviation), the test statistic will follow a standard normal distribution (z-distribution).
3. Identify the degrees of freedom: The degrees of freedom are specific to certain distributions, such as the t-distribution. For example, in a one-sample t-test, the degrees of freedom are determined by the sample size minus one (n - 1). In a chi-square test, the degrees of freedom are determined by the number of categories minus one. Consult the specific test you are performing to determine the degrees of freedom.
4. Look up the critical values: Once you know the significance level and distribution of the test statistic, you can consult the relevant table or use statistical software to find the critical values. These values represent the specific test statistic values that divide the rejection region from the non-rejection region. The rejection region consists of test statistic values that lead to the rejection of the null hypothesis.
Finding the standard error depends on the specific context and test you are working with. In general, the standard error is a measure of the variability or uncertainty in an estimator or statistic. Here are the basic steps to find the standard error:
1. Identify the formula: Each estimator or statistic has a specific formula for calculating the standard error. For example, the standard error of the mean can be calculated as the standard deviation divided by the square root of the sample size. The formula may change depending on the specific context and test.
2. Collect the necessary data: The calculation of the standard error typically requires relevant data. Collect the necessary data based on the specific formula you are using.
3. Substitute values into the formula: Once you have the necessary data, substitute the values into the formula to calculate the standard error.
4. Calculate the standard error: Perform the necessary calculations to find the standard error based on the specific formula.
If you provide more information on the specific context or test you are working with, I can give you a more detailed explanation of how to find the critical values and standard error.