Daily anxiety was measured on a scale from 1 (not at all anxious) to 5 (very anxious) in a random sa

Interpretation:
The 95% confidence interval can be interpreted as follows:
One can be 95% confident that the interval [4.06, 4.20] will hold the true average rating of daily anxiety.
In other words, if a similar procedure is carried out as in this study, and the 95% confidence interval is found for each study, then about 95% of those intervals would hold th true value.
Discussion:
The hypothesized mean is not mentioned here. Only the sample mean from the sample of n = 2,000 is given as M = 4.13.
Now, if M is the point estimate and E is the margin of error of a parameter, then, the confidence interval (CI) is: (M – E, M + E).
Here, M – E = 4.06; M + E = 4.20.
Thus,$E=\frac{[(M+E)–(M–E)]}{2}=\frac{[4.20–4.06]}{2}=0.07$.
The sample mean is 4.13, whereas the margin of error is 0.07, which is of a much smaller order than the sample mean. Thus, the point estimate, 4.13, appears to be quite precise at the 95% confidence level, with a margin of error of only 0.07.
Increasing the confidence level, suppose, from 95% to 99% widens the interval and thus, makes the estimate regarding the point estimate less precise.
Again, if the confidence level is decreased, say, from 95% to 90%, then the interval would become narrower. This makes the estimate regarding the point estimate more precise.
The hypothesized mean (or mean suggested by the null hypothesis) is not given here; only the observed sample mean is given.
As a result, we are unable to tell if the given 95% CI actually contains the hypothesized mean or not.
If the hypothesized mean is any value between 4.06 and 4.20, then it would mean that the calculated CI contains the true mean. Also, there is 95% confidence that the true mean is held within the given CI.
So, if the hypothesized mean is any value between 4.06 and 4.20, then you can conclude that there is a high likelihood that the hypothesized mean is true. In this case, you should fail to reject the null hypothesis in significance testing.
On the other hand, if the hypothesized mean is not any value between 4.06 and 4.20 and lies outside the interval, then it can be considered as quite less likely to be the true value, as there is 95% confidence for the interval to hold the true value. In that case, you should reject the null hypothesis in significance testing.

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