Problem-1 A bank claims that the average cash withdrawal prior to the holidays by customers was $4,100. However, when auditors randomly examined the statements of 50 random bank customers their average withdrawal for that period turned out to be $4,360. Use a value of 5% for the probability of a Type 1 error. If the standard deviation for withdrawals is $1,200, determine the following: a. Is there enough evidence from the sample of 50 customers to refute the bank's claim? Explain the reason for your answer. b. What is the p-value based the information given above? Show how you determined the answer. c. Repeat part 'a' if the $4,360 average withdrawal was based on 100 random bank customers' statements.

Problem-2 During a recent gasoline shortage, according to a random sample of 45 cars, the average wait time before filling gas at the local station was five and a half minutes. However, the owner of the gas station claimed that the average time spent by customers was five minutes. Use a value of 2% for the probability of a Type 1 error. If the standard deviation is 1.7 minutes per car, determine the following: a. Is there enough evidence from the sample of 45 cars to refute the gas station owner's claim? Explain the reason for your answer. b. What is the p-value based the information given above? Show how you determined the answer. c. Repeat part 'a' if the five and a half minute average wait time was based on 100 random cars.

Problem-3 Ken believes the average age of men who come to get a haircut at his barber shop is 40 or under. After getting age data from 60 customers who were randomly selected, the average age of the sample was computed as 50. Use a value of 2% for the probability of a Type 1 error. If the standard deviation for male customers' age is 8.0 years, determine the following: a. Is there enough evidence from the sample of 60 customers to challenge Ken's claim? Explain the reason for your answer. b. What is the p-value based the information given above? Show how you determined the answer. c. Repeat part 'a' if the average age of 50 was based on 100 random male customers