(1) A mutual funds manager claims that at least 70% of the stocks she selects will increase in price over the next year. We examined a sample of 200 of her selections over the 3 years. Our P-value turns out to be 0.03. Test an appropriate hypothesis. Which conclusion is appropriate? Explain a) There’s a 3% chance that the fund manager is correct? b) There’s a 97% chance that the fund manager is correct? c) There’s a 3% chance that a random sample could produce the results we observed, so it’s reasonable to conclude that the fund manager is correct. d) There’s a 3% chance that a random sample could produce the results we observed if p=0.7, so it’s reasonable to conclude that the fund manager is not correct e) There’s a 3% chance that the null hypothesis is correct
(2) Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of item that must be rejected, they will halt the assembly process until the problem can identified and repaired. A) Write null and alternative hypothesis for this problem B) What is the type I and Type II error in this context C) Which type of error would the factory owner consider more serious?
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