Final answer:
To find the margin of error along with the lower and upper limits, we typically use the formula E = Z*(σ/√n) and adjust the mean by this margin. The Z-score is determined by the desired confidence level and the standard deviation and sample size are given values. This answer assumes a 95% confidence level due to the lack of specific information provided regarding the confidence level.
Step-by-step explanation:
To calculate the margin of error, lower limit, and upper limit, we need to know the confidence level desired for the interval. However, since that information is not provided, a common confidence level such as 95% is typically assumed in these situations. The formula for the margin of error (E) at a certain confidence level, when the population standard deviation is known, is E = Z*(σ/√n), where Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
Here, the mean (μ) is 23.5 grams, the sample standard deviation (s) is 0.65 grams, and the sample size (n) is 14. However, since the population standard deviation is not provided, we would typically use the sample standard deviation in its place or use the t-distribution if the population standard deviation is unknown and the sample size is small. Assuming we are supposed to use the sample standard deviation and a Z-score for a 95% confidence level (which is approximately 1.96), the margin of error would be calculated as follows:
E = 1.96*(0.65/√14)
The lower limit is calculated by subtracting the margin of error from the mean, and the upper limit is calculated by adding the margin of error to the mean. Thus, the lower limit would be 23.5 - E and the upper limit would be 23.5 + E. These calculations would provide the bounds within which we are 95% confident the true mean weight of the cans of brined olives lies, rounded to four decimal places as per the question's instructions.