What price do farmers get for their watermelon crops? In the third week of July, a random sample of43farming regions gave a sample mean of= $6.88per 100 pounds of watermelon. Assume thatis known to be$1.92per 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 (in dollars). What is the margin of error (in dollars)? (For each answer, enter a number. Round your answers to two decimal places.)

lower limit$

upper limit$

margin of error$

(b)Find the sample size necessary for a 90% confidence level with maximal error of estimateE=0.37for the mean price per 100 pounds of watermelon. (Enter a number. 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 (in dollars). What is the margin of error (in dollars)?Hint:1 ton is 2000 pounds. (For each answer, enter a number. Round your answers to two decimal places.)

lower limit$

upper limit$

margin of error

2) You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Letxbe the age of the calf (in weeks), and letybe the weight of the calf (in kilograms).

x 1, 5,11, 16, 26, 36

y 39, 47, 73, 100, 150, 200

Complete parts (a) through (e), givenx=95,y=609,x²=2375,y²=81,559,x y=13,777,andr0.997.

(a)

Make a scatter diagram of the data. (Select the correct graph.)

B Verify the given sumsx,y,x²,y²,x y, and the value of the sample correlation coefficientr. (For each answer, enter a number. Round your value forrto three decimal places.)

x=

y=

x²=

y²=

x y=

r=

c Find, and. Then find the equation of the least-squares line=a+b x. (For each answer, enter a number. Round your answers forandto two decimal places. Round your answers foraandbto three decimal places.)

=

x bar =

=

y bar =

=

value of a coefficient

d Graph the least-squares line. Be sure to plot the point (,) as a point on the line. (Select the correct graph.)

e Find the value of the coefficient of determinationr². What percentage of the variation inycan beexplainedby the corresponding variation inxand the least-squares line? What percentage isunexplained? (For each answer, enter a number. Round your answer forr²to three decimal places. Round your answers for the percentages to one decimal place.)

r²=

explained =%

unexplained =%

f The calves you want to buy are15weeks old.What does the least-squares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.)