Hypothesis Testing

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Hypothesis Testing

• Dr. Stan Barrick
• Ed 250

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(No Transcript)
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Steps in Non-Classical Hypothesis Testing

• Write the null and alternate hypothesis.
• Choose the level of significance.
• Choose the correct test statistic.
• Obtain a random sample and calculate the p-value.
• If Pltthe level of significance, then reject the
  null hypothesis.
• Write the findings in English.

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Writing the Null and Alternate Hypothesis

• The null hypothesis is the hypothesis to be
  tested. This hypothesis is always of the form
• Based on a review of literature or experience the
  alternate hypothesis is the hypothesis to be
  proved. This hypothesis is one of three forms.

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Three Forms of the Alternate Hypothesis

• Two tailed no difference.
• Left tailed population
  mean1 is less that mean 2.
• Right tailed population mean1 is greater than
  mean 2.

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Choosing a Level of Significance (Alpha level)

• The usual levels of significance are as follows.
• 0.10
• 0.05
• 0.001
• This is also called the alpha level. The usual
  alpha level used in education is 0.05.

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Example 1

• I think that the reading achievement in my class
  of girls is better than boys. Let mean 1 be
  girls and mean 2 is boys.

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Example 2

• I think that the attitude toward math is better
  for boys than girls in my school. Let mean 1 be
  girls and mean 2 be boys.

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Example 3

• I am exploring the area of attendance. I have no
  idea who has better attendance boys or girls.
  Let mean 1 be girls and mean 2 be boys.

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Types of statistics for testing two groups.

• Z-test both groups are n larger than 30.
• T-test small samples and equal standard
  deviations.
• T-test small samples unequal standard
  deviations.
• T-test or z-test paired samples There is a
  logical pairing of samples (ie. brother-sister,
  identical twins, ...

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Achievement of Males and Females on the SAT

• I think that males score higher on the SAT than
  females in math. If mean 1 is males and mean 2
  is females, then write the null hypothesis and
  alternative hypothesis.
• Use a level of significance of 0.05.

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Data

• Males 510,520,480,600,550,400,320, 580
• Females 610,520,450,410,330,570,540,520.
• Should we use z-test, t-test, or paired t-test?
• T-test with equal or unequal standard deviations?

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Analysis

• Put the data in two separate columns of an XL
  spreadsheet.

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Analysis

• Click on tools Data analysis.
• Choose t-test equal standard deviations.
• High light the columns as usual.
• The mean difference is 0.

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Analysis
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Conclusion

• Is p-valuelt level of significance?
• Then accept the null hypothesis.
• English There is no evidence that there is a
  difference between the male SAT and female SAT.

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Example 2

• I have no idea who scores better on achievement
  tests males or females.
• Write a null hypothesis and alternate hypothesis.

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Example 2

• Data
• Males- 70,75,80,50,72,75,74,67,60,80
• Females-72,77,82,55,75,88,79,86,92,100
• Test at the .05 level of significance.

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Example 2