Question

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 45 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.90 per 100 pounds. (a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.) lower limit $ 6.59 Incorrect: Your answer is incorrect. upper limit $ 7.16 Incorrect: Your answer is incorrect. margin of error $ .28 Incorrect: Your answer is incorrect. (b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.27 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.) 134 Correct: Your answer is correct. farming regions (c) 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 $ 1978.93 Incorrect: Your answer is incorrect. upper limit $ 2149.07 Incorrect: Your answer is incorrect. margin of error $ 85.07 Incorrect: Your answer is incorrect.

Answer 1

For 90% confidence, .

a) Given , and .

The margin of error is:

The 90% confidence interval is:

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b) Given 7. The required sample size is:

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c) Given . Therefore:

Mean price would be

Standard deviation in price would be

and .

The margin of error is:

The 90% confidence interval is: