c8 What price do farmers get for their watermelon crops? In the third week of Ju
ID: 3264836 • Letter: C
Question
c8
What price do farmers get for their watermelon crops? In the third week of July, a random sample of 44 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that is known to be $1.94 per 100 pounds.
A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)
lower limit $_____ upper limit $_____ margin of error _____Explanation / Answer
lower limit = sample mean - z * sigma / sqrt(n) = 6.88 - 1.645*1.94/sqrt(44) = $6.4
upper limit = sample mean + z * sigma / sqrt(n) = 6.88 + 1.645*1.94/sqrt(44) = $7.36
Margin of error = 1.645 * 1.94 / sqrt(44) = $0.48
15 tons = 15 * 2000 = 30,000 pounds or 300 per 100 pounds
So, multiply all figures by 300
lower limit = $6.4 * 300 = 1920
upper limit = $7.36 * 300 = 2208
Margin of error = $0.48 * 300 = 144
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