Solve the following questions

1. The manufacturer ofan overthe-co'unter pain reliever claims that its product brings pain relief to headache suffers in less than 35 minutes, on average. To be able to make this claim in its television advertisements, the manufacturer was required by a particular television network to present evidence in support of the claim. The manufacturer reported that for a random sample of 45 headache sufferers, the mean time to relief was 3.3 minutes and the standard deviation was 66 seconds. Do these data support the manufacturers claim? Test using a level of significance of 0.05. I 2. The engineering department at Simms Software Inc. recently developed two chemical solutions designed to increase the usable life of computer disks. The data for the two solutions is summarized in the following table: Solution 1 X = 83.8 S1 = 13.68 n1 = 10 Solution 2 X=79.3 S2 = 6.71 n2 = 14 At the .10 significance level, can we conclude that there is a difference in the length of time the two types of treatment lasted?3. The Heartstopper restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean .of3 minutes and a standard deviation of 1 minute. The quality control department found that in a sample of 50 customers at the Warren Road Heartstopper that the mean waiting timewas 2.75 minutes. Can we conclude that the mean waiting time is 3 minutes? Use a: = .05 4. The research department at the home office of Superior Insurance conducts ongoing research on the cause of automobile accidents, the characteristics of the drivers, and so on. Specifically, they! looked at the proportion of married and single drivers who had at least one accident on their record. # with at least one Proportion accident At the 0.05 level, is there is significant difference in the proportions of single and married persons having at least one accident? ' Number of policies Married Single