Answer:
(a) 90% confidence interval for the population mean price (per 100 pounds) is ($6.34, $7.42)
Margin of error is $0.54
(b) The sample size is 172
(c) 90% confidence interval for the population mean cash value is ($1902.51, $2225.51)
Step-by-step explanation:
Confidence interval = mean + or - (t×sd)/√n
Mean = $6.88 per 100 pounds, sd = $1.94 per 100 pounds, n = 37, degree of freedom = n-1 = 37-1 = 36
t-value corresponding to 36 degrees of freedom and 90% confidence level is 1.688
(a) Lower limit = $6.88 - (1.688×$1.94)/√37 = $6.88 - $0.54 = $6.34
Upper limit = $6.88 + (1.688×$1.94)/√37 = $6.88 + $0.54 = $7.42
90% confidence interval is ($6.34, $7.42)
Margin of error (E) = (t×sd)/√n = (1.688×$1.94)/√37 = $0.54
(b) √n = (t×sd)/E = (1.688×$1.94)/0.25 = 13.10
n = 13.10^2 = 172
1 ton = 2000 pounds
15 tons = 15×2000 = 3000 pounds = 300 hundred pounds
Mean = $6.88×300 = $2064, sd = $1.94×300 = $582
Lower limit= $2064 - (1.688×$582)/√37 = $2064 - $161.51 = $1902.49
Upper limit= $2064 + (1.688×$582)/√37 = $2064+$161.51 = $2225.51
90% confidence interval is ($1902.49, $2225.51)
Margin of error = (1.688×$582)/√37 = $161.51
where, l be the length and b be the width
, r be the radius of the semicircle.