Suppose a certain species bird has an average weight of grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with grams. For a small group of 13 birds, find the margin of error for a 70% confidence interval for the average weights of these birds.

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Suppose a certain species bird has an average weight of grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with grams. For a small group of 10 birds, find the margin of error for a 70% confidence interval for the average weights of these birds.

To find the margin of error for a 70% confidence interval for the average weights of these birds, we need to determine the critical value associated with a 70% confidence level and then multiply it by the standard deviation of the population.

1. Determine the critical value:
The critical value represents the number of standard deviations away from the mean we need to go to capture the desired confidence level. For a 70% confidence level, we can use a standard normal distribution table or a statistical software to find the critical value. The critical value for a 70% confidence interval is approximately 1.04.

2. Calculate the margin of error:
The margin of error represents the range within which we expect the true population mean to lie. It is determined by multiplying the critical value by the standard deviation of the population, divided by the square root of the sample size.

In this case, we are given the standard deviation of the population ( grams) and the sample size (13). We can use these values to calculate the margin of error:

Margin of error = (Critical value) * (Standard deviation of population) / sqrt(Sample size)
Margin of error = 1.04 * grams / sqrt(13)

Evaluate this expression to find the margin of error.