Question 2: Match the 95% confidence interval boundaries with its corresponding method
1: one sample sign interval
2: one sample t interval

Question

BlackTom AI · Accepted Answer

Begin by restating what the prompt asks: we need to match each 95% confidence interval boundary to the corresponding method, with two items labeled 1) one sample sign interval and 2) one sample t interval.
However, the provided data shows two candidate interval bounds: (0.557, 0.654) ppb and (0.635, 0.934) ppb, but no explicit list of answer options to pair with each method. In other words, the matching pairs to select from are not present, so a definitive assignment cannot be made from the given information alone.
To evaluate which interval corresponds to which method in a typical context, one would consider how each interval is constructed and what it assumptions imply:
- One-sample t interval: This interval estimates a population mean under a normality (or approximate normality) assumption for the underlying data. It uses the sample mean, the sample standard deviation, and the critical t-value for the desired confidence level. The interval tends to be symmetric around the sample mean and its width reflects the estimated variability via s/√n, scaled by t_{alpha/2, df}.
- One-sample sign interval: This is a nonparametric interval based on the sign (above/below) of observations relative to a central value, often used with small samples or when the normality assumption is questionable. It does not rely on the sample standard deviation and typically yields a different, often wider or asymmetric interval depending on the sign-test distribution and the chosen central value.
If you had the actual answer options (i.e., which interval maps to which method), you would compare:
- The symmetry and center: a centered, symmetric interval around a sample mean is more characteristic of a t interval.
- The involvement of s (sample standard deviation) and n: a t interval uses s and n; a sign interval does not.
- The numerical width and bounds given the same data: in small samples, the two methods can produce noticeably different bounds.
Since the required pairing options are missing, you cannot complete the matching without the explicit option list. If you can provide the full set of answer options (the two method descriptions paired with each interval bound, or the list from which to choose), I can finalize the correct mapping and explain the reasoning for each pairing.
In practice, when you do obtain the options, proceed by:
- identifying which bound comes from a computation involving a t critical value and sample s, n (hinting at the t interval), and
- identifying which bound arises from a sign-test based construction (hinting at the sign interval).
Then assign (0.557, 0.654) ppb to the method whose construction matches those characteristics, and assign (0.635, 0.934) ppb to the other.

STAT 460, Section 001: Inter Appl Stat (22511--UP---P-STAT----460-------001-) Lab Quiz 9: Stat 460

Question 2: Match the 95% confidence interval boundaries with its corresponding method 1: one sample sign interval 2: one sample t interval

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