The farm's 11 tons of watermelon will have a 92% confidence interval mean cash value of $148.89, which is within the margin of error.
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and study results using the margin of error. Your findings will vary from the actual population figure by how many percentage points, as shown by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.
Here,
n = 38
x = 6.88
= 1.86
= 1-.90
= .10
/2 = .05
z(/2) = -1.64
-z(/2) = 1.64
P(-1.645 < z < 1.645) = .90
Margin of error= z(/2)(/√n)
= 1.645(1.86/√38)
= $.4963(300)
= $148.89
The margin of error for a farm brings 11 tons of watermelon to market with 92% confidence interval for the population mean cash value of this crop will be $148.89.
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