Ch10 - One Sample Tests - rjerz.com · One Sample Tests of ... •Conduct a test of hypothesis about a population mean. ... Ch10 - One Sample Tests Author: Rick Jerz Created Date:
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• Hypothesis• Test of hypothesis• Null hypothesis, alternative hypothesis• Level of significance• P-values• Reject or not reject• Type 1 and type 2 errors
• The mean length of a small counterbalance bar is 43 millimeters, and the production supervisor is concerned that the adjustments of the machine producing the bars has changed. He asks the engineering department to investigate.
• The company (or equipment) producing the bars says “The mean length is 43 millimeters.”
• A Hypothesis is a statement about the value of a population parameter developed for the purpose of testing. Examples of hypotheses made about a population parameter are:• The mean monthly income for systems analysts is
$3,625.• Twenty percent of all customers at Bovine’s Chop
House return for another meal within a month. • In our problem, the hypothesis, or statement
is “The process, or company thinks the bar length is 43 millimeters.”
• We can believe the claim.• Go on with life• Spend our time and energy elsewhere
• Alternatively, we might want to verify the claim by taking a sample and seeing what the sample data suggests.
• “Certainty” is only known if we had the entire population of data. Neither the claim nor the sample have the entire population, therefore, we have some “uncertainty.”
• The claim is called the “hypothesis.” Recognize that the claim does not have supporting evidence, meaning “none” or “null,” and is called the “null hypothesis.”
• The “alternative,” based upon sample data is referred to as the “alternative hypothesis.”
• We can use symbology to represent this:• H0: null hypothesis (the “0” might correspond to
“none”• H1: alternate hypothesis (the “1” might represent
“some” data)• H0 and H1 are mutually exclusive and collectively
exhaustive • H0 is always presumed to be true (correct) • H1 (you, the statistician) has the burden of proof
• I am willing to be wrong by rejecting the null hypothesis only 5% of the time, meaning a 5% level of significance.
• Assume that the p-value calculates to be 1%, meaning that I would be wrong by rejecting the null hypothesis only 1% of the time.
• Since the p-value is less than our level of significance, we reject the null hypothesis.
• If the p-value calculates to be greater than our level of significance, such as 22%, we would be wrong rejecting the null 22% of the time, but we only want to be wrong 5% of the time, so we do not reject the null.
“In recent years, spurred by the availability of computer software, additional information is often reported on the strength of the rejection or acceptance. This approach reports the probability of getting a value of the test statistic at least as extreme as the value actually obtained. This process compares the probability, called the p-value, with the significance level. If the p-value is smaller than the significance level, H0 is rejected. If it is larger than the significance level, H0 is not rejected.”