The margin of error of the 98.4% confidence interval for snapdragons is 3.71.
The midpoint of the range is calculated by adding the upper and lower bounds and then dividing by two. So, the sample mean is `(20.91 + 38.43) / 2 = 29.67`.
The margin of error is calculated by multiplying the critical value of z* (1.96 for a 98.4% confidence level) by the standard error of the mean. The formula for calculating the margin of error is:
`Margin of error z*(standard deviation/√n`).
The formula is `range/4 = 1.96 * standard deviation/√n`.Now, solve for the standard deviation:
`standard deviation = (range/4) * √n / 1.96`
Substituting the values: `(38.43 - 20.91)/4 = 1.96 * standard deviation/√n`
Simplifying the equation: `4.26 = (1.96*standard deviation)/√n`
Squaring both sides: `4.26^2 = 3.8416 = (1.96^2 * standard deviation^2)/n`
Substituting the value of the standard deviation: `3.8416 = (1.96^2 * ((38.43 - 20.91)/4)^2) / n`
Solving for n: `n = ((1.96^2 * ((38.43 - 20.91)/4)^2) / 3.8416) = 31.54`
Now that we know the sample size, we can calculate the standard error of the mean:
`standard error = standard deviation/√n = ((38.43 - 20.91)/4)/√31.54 = 1.89`.
The margin of error is `1.96 * 1.89 = 3.71`.
The 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). The margin of error of this confidence interval is 3.71.
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