Is this quarter fair?

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Practice

• You recently finished giving 5 Villanova students
  the MMPI paranoia measure. Determine if
  Villanova students paranoia score is
  significantly (? .10) different than the
  average paranoia of the population (? 56.1)?

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Scores
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Step 1 Write out Hypotheses

• Alternative hypothesis
• H1 ?sample 56.1
• Null hypothesis
• H0 ?sample 56.1

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Step 2 Calculate the Critical t

• N 5
• df 4
• ? .10
• tcrit 2.132

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Step 3 Draw Critical Region
tcrit 2.132
tcrit -2.132
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Step 4 Calculate t observed

• tobs (X - ?) / Sx

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Step 4 Calculate t observed

• tobs (X - ?) / Sx

Sx S / N
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Step 4 Calculate t observed

• tobs (X - ?) / Sx

S
-1
Sx S / N
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Step 4 Calculate t observed

• tobs (X - ?) / Sx

276
15306
4.21
5
5 - 1
Sx S / N
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Step 4 Calculate t observed

• tobs (X - ?) / Sx

1.88 4.21/ 5
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Step 4 Calculate t observed

• tobs (X - ?) / Sx
• -.48 (55.2 - 56.1) / 1.88

1.88 4.21/ 5
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Step 5 See if tobs falls in the critical region
tcrit 2.132
tcrit -2.132
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Step 5 See if tobs falls in the critical region
tcrit 2.132
tcrit -2.132
tobs -.48
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Step 6 Decision

• If tobs falls in the critical region
• Reject H0, and accept H1
• If tobs does not fall in the critical region
• Fail to reject H0

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Step 7 Put answer into words

• We fail to reject H0
• The average paranoia of Villanova students not
  statistically different (? .10) than the
  average paranoia of the population.

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One-tailed test

• In the examples given so far we have only
  examined if a sample mean is different than some
  value
• What if we want to see if the sample mean is
  higher or lower than some value
• This is called a one-tailed test

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Remember

• You recently finished giving 5 Villanova students
  the MMPI paranoia measure. Determine if
  Villanova students paranoia score is
  significantly (? .10) different than the
  average paranoia of the population (? 56.1)?

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Hypotheses

• Alternative hypothesis
• H1 ?sample 56.1
• Null hypothesis
• H0 ?sample 56.1

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What if. . .

• You recently finished giving 5 Villanova students
  the MMPI paranoia measure. Determine if
  Villanova students paranoia score is
  significantly (? .10) lower than the average
  paranoia of the population (? 56.1)?

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Hypotheses

• Alternative hypothesis
• H1 ?sample lt 56.1
• Null hypothesis
• H0 ?sample or gt 56.1

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Step 2 Calculate the Critical t

• N 5
• df 4
• ? .10
• Since this is a one-tail test use the
  one-tailed column
• Note one-tail directional test
• tcrit -1.533
• If H1 is lt then tcrit negative
• If H1 is gt then tcrit positive

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Step 3 Draw Critical Region
tcrit -1.533
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Step 4 Calculate t observed

• tobs (X - ?) / Sx

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Step 4 Calculate t observed

• tobs (X - ?) / Sx
• -.48 (55.2 - 56.1) / 1.88

1.88 4.21/ 5
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Step 5 See if tobs falls in the critical region
tcrit -1.533
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Step 5 See if tobs falls in the critical region
tcrit -1.533
tobs -.48
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Step 6 Decision

• If tobs falls in the critical region
• Reject H0, and accept H1
• If tobs does not fall in the critical region
• Fail to reject H0

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Step 7 Put answer into words

• We fail to reject H0
• The average paranoia of Villanova students is not
  statistically less then (? .10) the average
  paranoia of the population.