Question

A standardized test was used to asses the level of depression in a group of patients on a cardiac unit. The results yield a mean of 14.60 with confidence interval of 14.55 and 14.65. This presented confidence interval is (show work)

a. less, precise, but higher confidence that 14.20 and 15.00

b. more precise, but lower confidence that 14.20 and 15.00

c. less precise, but has lower confidence that 14.20 and 15.00 d.more precise, but has higher confidence that 14.20 and 15.00

e. indeterminate, because the degree of confidence is not specified

Answer 1

The confidence interval of 14.55 to 14.65 is more precise than the interval of 14.20 to 15.00 due to its narrower range. The level of confidence cannot be determined without additional information.

Step-by-step explanation:

The confidence interval provided is more precise, but it has the same level of confidence as a wider interval. The precision of a confidence interval refers to the range it covers, with a smaller range indicating higher precision. The provided interval ranges from 14.55 to 14.65, while the comparative interval ranges from 14.20 to 15.00. An interval of 0.10 units (from the provided interval) is narrower and thus more precise than an interval of 0.80 units (from the comparative interval).

However, the confidence level is not indicated for the provided interval, and without this information, we cannot say whether the confidence level of the provided interval is higher or lower than any other. The confidence level pertains to the probability that the interval will include the true population parameter if the study were repeated multiple times. Typically, as the level of confidence increases, the interval widens because you are including a greater range to ensure the true value is captured.

In summary, the correct answer is that the confidence interval of 14.55 to 14.65 is more precise, but without further information, we cannot determine if it has a higher or lower confidence level compared to the interval of 14.20 to 15.00.