hypothesis lecture

8/4/2019 Hypothesis Lecture

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August 25, 2011Biostatistics

Hypothesis Testing

Hypothesis A statement of belief used in evaluation ofpopulation values.

Null Hypothesis (H0) a claim that is no difference betweenthe population mean and the hypothesized value 0.

Steps:

1.) State the hypothesis.

2.) Determine the level of significance3.) Determine critical values4.) Compute the test statistic5.) Decision: reject H0 if,- | computed value | > | critical value |6.) Conclusion.

Alternative Hypothesis a claim that disagrees with the nullhypothesis. If it is rejected, we are left with no choice but tofail to reject the alternative hypothesis that is not equal to 0.Referred to as research hypothesis.

Test statistic a statistic used to determine the relativeposition of the mean in the hypothesized probabilitydistribution of the sample means.

Critical Region is the region on the far end of thedistribution. If only one end of the distribution, commonlytermed the tail, is involved, the region is referred to as one-tailed test; if both ends are involved the region is called two-tail test. When computed value falls into the critical region,we reject the null hypothesis. The region is sometimes calledthe rejection region. The probability that a test statistics falls inthe critical region is denoted by .

Critical Value is the number that divides the normaldistribution into the region where we will reject the nullhypothesis and the region where we fail to reject the nullhypothesis.

Significance Level is the level that corresponds to the areain the critical region. By choice, this area is usually small; theimplication is that results falling in it to do so infrequently.Consequently, such events are deemed unusual or in thelanguage of statisticians are usually significant. When a teststatistics falls in this area, the result referred to as significantlevel at the level.

Nonrejection Region is the region of the samplingdistribution not included in the ; that is the region located

under the middle portion of the graph.

Test Significance A procedure used to establish the validityof a claim determining whether the test statistic falls in the


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critical region. If it does, the results are referred to assignificant; this test is sometimes called the hypothesis test.

Example:In the 1970s, the US male population between 20 -29

years had body weights with an approximate lognormaldistribution with mean 170 pounds and standard deviation 40.To test whether body weight has increased since that time, wetake an SRS of men from the current population, calculatetheir mean weight and compare to the statistical mean.

- What is the null hypothesis?- What is the alternative hypothesis?

H0: =170H1: 170 > 170

Type I and Type II Errors

There are two possible decisions:1.) H0 is false and consequently is rejected2.) H0 is true and consequently fail to reject it

Type I error probability of rejecting a true null hypothesis.Type II error probability of failing to reject a false nullhypothesis.

P(Accept H0 / H0 is true) = 1 P(Reject H0 / H0 is false) = 1

Example

Test at the 5% level, whether the sample value of 72comes from a normal distribution with a mean of 55 and avariance of 144.

- What is the probability of a type 1 error?

Answer: 5%


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A die is suspected of being biased towards the six, totest the die is rolled 60 times and the two hypotheses are putforward.

H0: = 1/6H1: >1/6

It is decided to reject the null hypothesis if there are15.5 or more sixes in the 60 rolls of the die. Find theprobability of a type I error when mean is 10 and 2 = 499.8

Z= 15.5 10499.8/60

Z = 15.5 10

8.33Answer: 1.91

Find the area:1.91 0.0280

hypothesis lecture

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