True or False?
In a Chi-Square distribution, when the degrees of freedom increase, the test statistic also increases (assuming all other variables are held constant.)
In a T-test for the population mean (standard deviation is unknown), the test statistic is equal to zero if the sample mean is equivalent to the population mean.
I really appreciate any help!
In a Chi-Square distribution, the test statistic is determined by the degrees of freedom. The test statistic does not necessarily increase as the degrees of freedom increase. Instead, the shape of the Chi-Square distribution changes with different degrees of freedom. As the degrees of freedom increase, the distribution becomes less skewed and approaches a normal distribution.
To evaluate whether the test statistic increases as the degrees of freedom increase, you can refer to the Chi-Square table or use statistical software. By comparing the critical values for various degrees of freedom, you can determine whether the test statistic increases.
Regarding the second statement, in a T-test for the population mean (when the standard deviation is unknown), the test statistic is not equal to zero when the sample mean is equivalent to the population mean. The T-test calculates the difference between the sample mean and the hypothesized population mean, and compares it to the standard deviation of the sample mean.
The formula for the T-test divides the difference between the sample mean and the hypothesized population mean by the standard error of the sample mean. If the sample mean is equivalent to the population mean, the test statistic will be 0. However, this is not a common scenario in hypothesis testing.
To perform a T-test, you need to have the sample mean, the hypothesized population mean, the sample standard deviation, and the sample size. By plugging these values into the T-test formula, you can calculate the test statistic and compare it to the critical value to make conclusions about the hypothesis.
I hope this explanation helps! Let me know if you have any more questions.