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

Yes, df = n-1

For two-tailed test:

Ho: mean = X
Ha: mean ≠ X

For one-tailed test:

Ho: mean < or = X
Ha: mean > X

or

Ho: mean > or = X
Ha: mean < X

Ho = null hypothesis
Ha = alternative hypothesis

how do we know it is one tailed test or two tailed test?

What are your hypotheses? That determines difference between one-tailed and two-tailed (see my previous post).

the average weekly earnings of a production worker were $424. to know if wages, on average, have gone up since that time. To test this, you sample 64 production workers, and determine that their average salary is $432.69, with a sample standard deviation of $33.90. Use a 0.05 level of significance .carry out test .

is it t test or z test ? how would we know

in this case one tailed or two tailed how can we know?

If a population proportion is 0.29 and if the sample size is 120, 25% of the time the sample proportion will be less than what value if you are taking random samples?

Round your answer to 2 decimal places, the tolerance is +/-0.01.

To calculate the exact t-value using the sample standard deviation, sample mean, and sample size, follow these steps:

1. Determine the sample mean and sample standard deviation from your data.

2. Calculate the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size. The formula for SEM is: SEM = sample standard deviation / sqrt(sample size).

3. Determine the degrees of freedom (df) by subtracting 1 from the sample size. This assumes you are working with an independent samples t-test or a one-sample t-test.

4. Calculate the t-value by dividing the difference between the sample mean and the null hypothesis value by the standard error of the mean: t = (sample mean - null hypothesis value) / SEM.

To use the t-score table for finding the exact t-value:

1. Determine the degrees of freedom (df) from step 3.

2. Identify whether you have a one-tailed or two-tailed test. This is determined by the research hypothesis and what you are trying to investigate.

- For a one-tailed test: If your research hypothesis is directional (e.g., "X is greater than Y" or "X is less than Y"), use the one-tailed column in the t-score table.
- For a two-tailed test: If your research hypothesis is non-directional (e.g., "X is different from Y"), use the two-tailed column in the t-score table.

3. Determine the significance level (alpha) you want to use for your test (e.g., 0.05 or 0.01).

4. Look up the critical t-value in the appropriate column based on the degrees of freedom and significance level. This table will provide both positive and negative critical values for a two-tailed test and only a positive critical value for a one-tailed test.

To determine if it is a one-tailed or two-tailed test:

1. Look at your null and alternative hypotheses.

- If your research hypothesis only states a change in one direction (e.g., "X is greater than Y" or "X is less than Y"), then it is a one-tailed test.
- If your research hypothesis states a change in any direction (e.g., "X is different from Y"), then it is a two-tailed test.

Remember, the choice of one-tailed or two-tailed test should be based on the specific research question and hypothesis being tested.