1. A Call-center claims that the average time a customer waits on hold is less than 5 minutes. To test this claim, a random sample of 35 customer calls is selected. The average wait time for the sample is 4.78 minutes with a sample standard deviation of 1.8 minutes. Test the company's claim at a 5% level of significance. What is your conclusion?
2. A government agency claims that more than 50% of U.S. tax returns were filed electronically last year. To test this claim, a random sample of 150 tax returns was selected and it showed that 86 were filed electronically. Test the claim at a 5% level of significance. What is the p-value for this test? What is your conclusion?
3. A tire manufacturer produces tires that are believed to have a mean life of at least 35,000 miles when the production process is working correctly. Based on past experience, the population standard deviation of the lifetime of the tires is 4,500 miles. Assume a level of significance for testing of 5%, and a random sample of 35 tires:
A) What would be the consequences of making a Type II error in this problem?
B) Compute the Probability of making a Type II error if the true population mean is 33,000 miles.