1. A researcher believes that the average size of farms in the U.S. has increased from the 2002 mean of 471 acres. She took a sample of 23 farms in 2011 to test her belief and found a sample mean of 487 acres and a sample standard deviation of 46.9 acres. At a 5% level of significance, test the researcher’s claim. What is your conclusion?
2. A study by Hewitt Associates showed that 79% of companies offer employees flexible scheduling. Suppose a researcher believes that in accounting firms this figure is lower. The researcher randomly selects 410 accounting firms and determines that 304 of these firms have flexible scheduling. At a 1% level of significance, does your test show enough evidence to conclude that a significantly lower percentage of accounting firms offer employees flexible scheduling? What is the p-value for this test?
3. The American Lighting Company developed a new light bulb that it believes will last at least 700 hours on average. A test is to be conducted using a random sample of 50 bulbs, and a 1% level of significance. Assume that the population standard deviation is 10 hours. What are the consequences of making a type II error? What is the probability of making a Type II error if the true population mean is 695 hours?