Example one A researcher believes that in recent years women have been getting taller. She knows that 10 years ago the average height of young adult women living in her city was 63 inches. The standard deviation is unknown. She randomly selects eight

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Example oneA researcher believes that in recent
years women have been getting taller. She knows
that 10 years ago the average height of young
adult women living in her city was 63 inches.
The standard deviation is unknown. She randomly
selects eight young adult women currently
residing in her city and finds that the average
height of these women is 64.25 inches. The
standard deviation of this sample is 2.55.
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What are the critical pieces that will tell us
which t-test to use?
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Example oneA researcher believes that in recent
years women have been getting taller. She knows
that 10 years ago the average height of young
adult women living in her city was 63 inches.
The standard deviation is unknown. She randomly
selects eight young adult women currently
residing in her city and finds that the average
height of these women is 64.25 inches. The
standard deviation of this sample is 2.55.

• µ63 (population average)
• n8 (number in this sample)
• 64.25 (average of this sample)
• S2.55 (standard deviation of this sample)

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Which test to do?

• We dont know the population SD so we cant find
  a z-score.
• We have only one sample, so we need to use a
  t-test for single samples.
  

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Statistical Hypothesis Statements

• H0 u 63 (This sample is from the population
  whose mean is 63).
• H1 u ? 63(This sample is not from the
  population whose mean is 63).

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t-test for single samples
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t-test for single samples

• df n-1n 8 df n-1 8-1
  7 critical value2.365 (from
  t-table)

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t-test for single samples

• Since computed t is less than critical t, (1.39
  lt 2.365),We accept H0(H0 u 63)Women
  continue to be the same height as they were ten
  years ago.

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Ex.2 A psychologist is interested in
determining whether memory is affected by sleep
loss. 12 normal subjects are randomly selected
and assigned to two groups of 6 each. Group one
gets a normal amount of sleep (7-8 hours). This
groups mean score is 70.17 with a standard
deviation of 3.18. Group two is sleep deprived
for 24 hours. They have an average score of
65.33 and a standard deviation of 4.18.
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• A psychologist is interested in determining
  whether memory is affected by sleep loss. 12
  normal subjects are randomly selected and
  assigned to two groups of 6 each. Group one gets
  a normal amount of sleep (7-8 hours). This
  groups mean score is 70.17 with a standard
  deviation of 3.18. Group two is sleep deprived
  for 24 hours. They have an average score of
  65.33 and a standard deviation of 4.18.
  
  S13.18 S24.18

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Which test to do?

• Cant do a z-score because we dont know the
  standard dev. of the population
• Cant do a t-test for single samples because we
  have two samples.
• Because we have two samples, we have to do a
  t-test for 2 independent samples

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Statistical hypothesis statements

• H0 u1 u2 The two samples are from the same
  population.
• H1 u1 ? u2The two samples are not from the same
  population.

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t-test for independent samples

• Can use shortened formula because the two samples
  are of equal size.

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t-test for independent samples
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t-test for independent samples

• t 2.26 (computed t value)
• For independent samples t-testdf n1 n2-2
  66-2 10critical t value 2.228 (from
  t-table)

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t-test for independent samples

• Since computed t is greater than critical T,
  (2.26 gt 2.228),We reject H0Accept H1 u1 ? u2
  The two groups are significantly different from
  each other. There is an effect of sleep
  deprivation on memory.

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Example 3

• To motivate citizens to conserve fuel, the
  government would like to mount a nationwide
  campaign. Before doing so however, they wish to
  test the effectiveness of the campaign. Twelve
  families are selected and their consumption of
  fuel before the campaign and afterward is
  monitored.

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What kind of t-test should be done here?

• To motivate citizens to conserve fuel, the
  government would like to mount a nationwide
  campaign. Before doing so however, they wish to
  test the effectiveness of the campaign. Twelve
  families are selected and their consumption of
  fuel before the campaign and afterward is
  monitored.

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t-test for matched samples

• Something in the problem talking about subjects
  matched or that the same subjects took a test
  twice (before and after) or same subjects taking
  test at time 1 and time 2

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t-test for matched samples

• From raw data (Time 1 and Time 2) 1. Find
  difference between those measurements for each
  subject. 2. Find average of the differences.3.
  Find the standard deviation of the
  differences.4. Use this S to find the standard
  error of the differences,

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t-test for matched samples

• (continued)5. Solve for t. 6. Compare this
  computed t to critical t (dfn-1) from
  t-table to see if significant difference between
  before and after scores.