What price do farmers get for their watermelon crops? In the third week of July,

Question

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 36 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that is known to be $1.88 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.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.37 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
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.)

Explanation / Answer

here std error =std deviation/(n)1/2 =0.3133

for 90% CI, z=1.645

hence margin of error =z*std error =0.5154

lower confidence interval =sample mean -margin of error =6.3646

upper confidence interval =sample mean -margin of error =7.3954

b)sample sizer=(z*std deviation/E)2 =~70

c) here n=15*2000/100=300

margin of errror =0.1785

lower confidence interval =6.7015

upper confidence interval =7.0585

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