Someone please help me solve this question, please show all the working out (in step by step) if possible please work out in paper.

Please draw the graph clearly as well. Thank you very. Please help me. I'm really having trouble solving this one.

PS: Importantly please use the same formula as used in (information)

Question

• Determine a 90% confidence interval for the sample data whenis known.
• State and testappropriatehypotheses for evaluating the squareness of the origami paper at a 1% level of significance whenis unknown for an SRS of size n=8.

Important equations For Population Mean: N E Xi u = For Sample Mean: n E Xi X = El n For Population Standard Deviation: N E(Xi -M)2 0 = i=1 N For Sample Standard Deviation: n E (X; - X)2 i=1 S : n - 1Explanation: Given: N = 12 (popufation) 71 = 8 (sample) For Mean of Population: Using all the given diagonal lengths for the population _ 247 + 247.5 + 247.5 + 247.5 + 247.3 + 248.9 + 247 + 247.5 + 248.9 + 247.5 + 249 + 247.5 \"diagonal 12 \"diagonal = 247.7583 mm For anlation Standard Deviation: where 257x.- 247.7583? = (247 247.7583? + (247.5 247.7583? + (247.5 247.7583? + (247.5 247.7583? + (247.3 247.7583? + (248.9 247.7583? + (247 247.7583? + (247.5 247.7583? + (248.9 247.7583? + (247.5 247.7583? + (249 247.7583? + (247.5 247.7583? Egan- 247.7583? = 5.909157 Then. a = w = 0.701734mm For Sample Mean: Belew is the observations that were assigned to the top 8 random numbers: Diagonal Length 247 247.5 242.5 249 247.5 248.9 248.9 242.5 f _ 24? + 247.5 + 242.5 + 249 + 28,415 + 248.9 + 248.9 + 242.5 X = 247.975 mm For Sample Standard Deviation: where 2:721,- 247.975? = (247 247.975? + (247.5 247.975? + (247.5 247.975? + (249 247.975? + (247.5 247.975? + (248.9 247.975? + {248.9 247.975? + (247.5 247.975? 2:10:7- 247.975? = 4.615 Then