Some of my classmates are having issues with this assignment and could really use the help. We need help with all of the questions and all the information is on the attached pictures except one piece of information for question 5 which is that our professor wants us to use 3 different critical values: 1%, 5%, and 10%. Thank you :)

1. Cans of lemonade are lled by a machine which is set to dispense an amount which is normally distributed with mean 3301111 and standard deviation 2.4m]. A quality control manager suspects that the machine is over- dispensing and tests a random sample of 8 cans. The volume of the contents, in ml, are as follows: 329 32? 331 326 334 343 328 339 Test at the 2 % signicance level, whether the manager's suspicion is justied. 2. A drug company tested a new pain-relieving drug on a random sample of 100 headaches sufferers. Of these, 25% said that their headache was relieved by the drug. lWith the currently marketed drug, 65% of users say that their headaches were relieved by it. Test at the 4% level, whether the new drug will have a great proportion of satisfied users. 3. A food processor produces large quantities of _] ars of Jam. In each batch, the gross weight of a jar is known to be normally distributed with standard deviation 2.5g. (The gross weight is the weight of the jar plus the weight of the jam.) The gross weights, in grams, of a random sample from a particular batch were: 5l44355143652 4965949149T51 506436493490484 4945l448? 50T496505493499 4. A croupier at a casino is accused of using a die which is biased towards showing a six. The management tests the die by rolling it 500 times, and 98 sixes were recorded. At the 5% significance level, does this result support the compliant? To try to eliminate complaints, a new die is suggested. This die is also rolled 500 times, and 90 sixes were recorded. a. Calculate a 99% condence interval for the proportions of sixes the die will show. b. At a 5% signicance level, does this die show bias towards a six? 5. A study of seat belt users and non-users yielded the randome selected sample data surmnarized in the given table. Test the claim that the amount of smoking is independent of seatbelt use. A plausible theory is that people who smoke more are less concerned about their health and safety and are therefore less inclined to wear seathelts. Is this theo su - orted b the sample data? [I day ]- [4 days 15-34 days 35 and over days Wear seatbelts [75 2!} 42 6 Doesn't wear seatbelts [49 1? 4l '9