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Hello again,

Please see the question and let me know if you are able to answer it. If you are not able to answer it, I can settle with that answer as well.

Here is my initial question:

Let me start by mentioning that my question is not about the t-test, but rather CIs for the mean. I'm familiar with interpreting the t-test.

When calculating confidence intervals for the mean, we find a t-value. Let's say we find a t-value of 44 when comparing the sample mean and sample standard deviation of 56.7 and 0.37, respectively. The population mean is 54.5 for the scenario.

How would we interpret the t-value in general terms?

I understand the t-test is comparing means, but I'm not sure that the t-value in the context of the CI would be interpreted the same. I also understand how to interpret the scenario in terms of the CI. It is the t-value specifically here that I'm trying to interpret correctly (although not part of the assignment).

Here was the response:

Step 1
The 95% of confidence interval for the mean tell us the range of values that 95% certain contains the true mean population.
While calculating the t confidence interval the margin of error is calculated using the t value as shown below.

Step 2
Margin of error is the error term, which is the deviation from sample mean with in which we are certain that population mean will fall.

So while calculating the confidence interval we use the t value in calculation of margin of error. If the margin of error is small then, the result is accurate and if the margin of error is large then the results are not considered as accurate.

To find the t value we need level of significance and degree of freedom. We use the same t value in hypothesis test and confidence interval.
In hypothesis test we test if the claim and in confidence interval we estimate the range of values for population parameter so that we are certain that true value lie with in.

I am just wanting to know how to state in words what the "44" indicates for the t-value. In a t-test, I understand its interpretation. In calculating the t-value, we are calculating the quotient of the 'difference between the means' and the 'standard deviation of the means.'

But if somebody asked you for an interpretation of just the '44' of the t-value, what would it be?

The t-value of a t-test has a specific interpretation; I understand that interpretation. I'm not sure if the interpretation for the t-value in the CI here is the same.

Again, if you are not sure how we would speak to just the '44' of the t-value, please let me know.

Thank you.

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Step 1

Note:

Hey there! Thank you for bringing up your doubt. We would try to answer to the best of our ability this time to help you clarify your doubt.

Step 2

The t-value for test statistic:

The t-value in the confidence interval (CI) is slightly different from the t-value in the test statistic. Let us understand how.

Suppose you are conducting the one-sample t-test. It means that you don’t know the population standard deviation and use the sample standard deviation (s) instead; the sample size, n is also quite small, that is, less than 30, and the data distribution is reasonably close to normal.

The “t-value” in a t-test, is the t-statistic:

t = (μ) / (s/√n).

This t-value is entirely dependent on your data or the information that you have regarding the population, such as, the hypothesized value of μ. The calculation of this t-value has noth...

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