Hi. Please give full explainations to these post questions.

Lesson 2.3 Discussion

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Post a response to the following statements/questions:

1. For any given hypothesis test, that is, for any specification of the null and alternative hypotheses, explain why you could make only a type I error or a type II error, but not both. When would you make a type I error? When would you make a type II error? Answer as generally as possible.
2. Give an example of when a one-sided test on a population mean would make more sense than a two-tailed test. Give an example of the opposite. In general, why do we say that there is no statistical way to decide whether a test should be run as a one-tailed test or a two-tailed test?
3. Consider the situation where you are testing the null hypothesis that a population mean is less than or equal to 100 versus a one-tailed alternative. A sample size formula might indicate the sample size needed to make the power at least 0.90, when the true mean is 103. What are the trade-offs here? Essentially, what is the advantage of a larger sample size?
4. Suppose that you wish to test a researcher's claim that the mean height in meters of a normally distributed population of rosebushes at a nursery has increased from its commonly accepted value of 1.60. To carry out this test, you obtain a random sample of size 150 from this population. This sample yields a mean of 1.80 and a standard deviation of 1.30. What are the appropriate null and alternative hypotheses? Is this a one-tailed or two-tailed test?
5. Suppose that you wish to test a manager's claim that the proportion of defective items generated by a particular production process has decreased from its long-run historical value of 0.30. To carry out this test, you obtain a random sample of 300 items produced through this process. The test indicates apvalue of 0.01. What exactly is thispvalue telling you? At what levels of significance can you reject the null hypothesis?