Final answer:
To find the margin of error for the 98.58% confidence interval, we use the sample proportion of car owners with brand loyalty (0.8102), locate the Z-score for the given confidence level, and apply the margin of error formula. The final value is not provided since the Z-score is not specified.
Step-by-step explanation:
To calculate the margin of error for the 98.58% confidence interval on the proportion of car owners who made their purchase primarily based on brand loyalty, we first need to identify the sample proportion. In this case, 794 out of 980 car owners have shown brand loyalty, so the sample proportion (p') is 794/980 ≈ 0.8102.
The formula for the margin of error (ME) at a given confidence level is:
ME = Z * sqrt((p'(1 - p')) / n)
Where:
- Z is the Z-score corresponding to the desired confidence level.
- p' is the sample proportion.
- n is the sample size.
The Z-score for a 98.58% confidence level needs to be found in a Z-table or calculated using statistical software. Assuming we have the Z-score, we can substitute all the values into the formula to find the margin of error.
Without the actual Z-score value provided, this is as far as we can go in calculating the margin of error for this problem. It is important to round the final answer appropriately, according to standard rounding rules for statistics.