Hypothesis Testing, Statistical Inference, and Regression Analysis

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I have answered the questions in your posting in the attached MS Word doc. Good luck.

Hypothesis Testing, Statistical Inference and Regression Analysis

1. Explain the difference between the null and alternative hypothesis. Which one can be proven in a statistical sense?
The main difference between the null hypothesis and the alternative hypothesis is that the null ALWAYS allows equality to happen and the alternative NEVER allows equality to happen. In a basic, one-sample hypothesis test both types of hypotheses are mathematical statements about the values of some population parameter (like a population mean value or a population proportion for example). The null assumes that nothing has changed. The alternative basically is stating that a change has occurred. To be honest, neither hypothesis can be "proven", but in a statistical sense, since you end up rejecting the null hypothesis only when the data provides enough evidence (in a statistical sense) that the null is NOT true (which effectively means that you DO believe that the alternative hypothesis is the one that is "true" ... or at least is supported by the data), you could argue that the alternative may be "proven" in a statistical sense.

2. What are the differences between one- and two- sample hypothesis tests? Describe the correct mathematical form for specifying the null and alternative hypotheses for both types of tests.
One obvious difference between one- and two-sample hypothesis test is the number of samples required to perform each kind of test (one versus two). Another big difference is that the point of a one-sample hypothesis test is to be able to say something intelligent (based on data) about the value of some population parameter (like the population mean or the population proportion). In a two-sample hypothesis test the goal is to compare the parameter that describes one population to the same parameter that describes the other population to determine if they are, or are NOT significantly different.
One-Sample Tests on a Population Mean value:
Two-tailed test Lower Tail One-Tailed Test Upper Tail One-Tailed Test

One-Sample Tests on a Population Proportion:
Two-tailed test Lower Tail One-Tailed Test Upper Tail One-Tailed ...