Means 3. A certain brand of apple juice is supposed to have 64 ounces of iuice. The target mean amount of juice is 64.05 ounces. However, the lling machine is not precise, and the exact amount varies from bottle to bottle. The quality control manager wishes to verify that the mean amount in each bottle is 64.05 ounces so that she can be sure that the machine is not over-filling or under-filling. She randomly samples 12 bottles of juice and measures the content and obtains the following data: 64.03, 63.97, 63.95, 64.06, 64, 64.05, 64.08, 64.03, 63.94, 64.01, 64.06, 64.01 Should the assembly line be shut dewn so that themachine can be recalibrated? Use (1:0.01 level of significance. State the conclusion. b. Find a 99% condence interval for the true mean amount of juice in these bottles. State the conclusion. 4. Researchers wanted to check if carpeted rooms in hospitais contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish for eight carpeted and eight un carpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results are presented in the table. [Measured as bacteria per cubic foot] Carpeted: 11.8, 10.8, 8.2, 10.1, 7.1, 14.6, 13.0, 14.0 Uncarpeted: 12.1, 12.0, 8.3, 11.1, 3.8, 10.1, 7.2, 13.? Do carpeted rooms have more bacteria than uncarpeted rooms at (120.05 level of signicanoe. State the conclusion. Goodnessof Fit 5. A buyer for a t-shirt shop wants to compare the proportion of t-shirts of each size that are sold to the proportion that were ordered. The buyer counts the number of tshirts of each size that are sold in a week. size 30ch Percentage ordered Does the distribution of the sold items folIOw the distribution of the ordered items? state the conclusion