how to know exact t value using sample standard deviation and sample mean and sample size
i think df is sample size -1 .
we usually use approx value but to use exact value how to use t score table.
and how we conclude whether it is two tailed test or one tailed test .
(i f the problem asks for exact increase or decrease ,is it one tailed test ,i guess so ,)
please clarify my doubts
To calculate the exact t-value using sample standard deviation, sample mean, and sample size, you need to follow these steps:
1. Calculate the standard error of the mean (SEM) using the formula SEM = sample standard deviation / √sample size.
2. Calculate the difference between the sample mean and the null hypothesis mean.
3. Divide the difference obtained in step 2 by the SEM calculated in step 1.
The resulting value is the t-value, which represents the number of standard deviations the sample mean is away from the null hypothesis mean.
Regarding the degrees of freedom (df), you are correct that it is calculated as the sample size minus one (df = sample size - 1). The degrees of freedom are important when using the t-distribution for hypothesis testing and determining critical values from the t-score table.
To find the exact t-value from the t-score table, you need to know the significance level (alpha) and the degrees of freedom (df). Look up the corresponding critical value in the table.
For instance, let's say you have a two-tailed test with alpha = 0.05 and df = n - 1. In this case, you would split the alpha value into two equal parts for each tail, i.e., 0.025 for each tail. Then, consult the t-score table with the corresponding degrees of freedom (df) to find the critical values for both tails.
To determine whether you need to perform a one-tailed or two-tailed test, you need to consider the research question and hypotheses. If the question specifically asks for an exact increase or decrease, it suggests a one-tailed test. However, the final determination should be made based on the specific context and the nature of the problem.
Remember, a two-tailed test is used when you are interested in whether the sample mean significantly differs from the null hypothesis mean in either direction, while a one-tailed test is used when you are interested in a significant difference in only one direction (either an increase or a decrease).
It's important to carefully read the problem and clearly define your research question and hypotheses to determine whether a one-tailed or two-tailed test should be used.