# Statistics Essay

3356 Words Dec 21st, 2013 14 Pages
WISE-International Master

Hypothesis Testing

A hypothesis is a claim (conjecture/assumption) about a population parameter:
  

population mean population proportion It is always about a population parameter, not a sample statistic

A Common Theme
Check the merits of this hypothesis based on sample information sample A hypothesis is formed about some population parameter

infer

Hypothesis testing provides a general framework for approaching such inference problems

ˆ

The Null Hypothesis

Suppose that some hypothesis has been formed about the population parameter  and that this hypothesis will be believed unless sufficient contrary evidence is produced.

This
- In the absence of evidence to question this claim, we maintain this hypothesis - When sample information is collected, this maintained hypothesis is put in jeopardy, or tested. - If the maintained hypothesis is not supported, then some alternative hypothesis must be accepted - When we carry out a hypothesis test, we formulate an alternative hypothesis against which the null hypothesis is tested.

The manufacturer of a new product claims that his product will increase output per machine by at least 29 units per hour. A line manager adopts the product on 15 of his machines, and finds that the average increase was only 26 with a standard deviation of 6.2.

B

Having specified a null and alternative hypothesis and collected sample information, a decision concerning the null must be made. We either reject the null in favor of the alternative or accept the null. We need some decision rule to reach one of these conclusions.

Recall: A manufacturer who produces boxes of cereal claims that, on average, the contents weigh at least 20 ounces. - Suppose we collected a random sample and the sample mean weight is much less than 20 ounces. - We might then suspect the validity of the claim that the population mean is at least 20 ounces. - The decision rule would then involve the rejection of this null hypothesis if the sample mean

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