Tests of Significance

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Tests of Significance
Part II
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Steps for Tests of Significance

• 1. Identify the population of interest and the
  parameter you want to draw conclusions about.
  State null and alternative hypotheses in words
  and symbols.

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Steps for Tests of Significance

• 2. Choose the appropriate inference procedure.
  Verify the conditions for using the selected
  procedure.

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Steps for Tests of Significance

• 3. If the conditions are met, carry out the
  inference procedure. Calculate the test
  statistic. Find the p-value.

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Steps for Tests of Significance

• 4. Interpret your results in the context of the
  problem.

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Tests for Population Mean

• One-tailed when Ha µ gt µ0
• Or when Ha µ lt µ0
• Which tail is which?

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Tests for Population Mean

• Two-sided or two-tailed
• Ha µ ? µ0

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Executives Blood Pressures

• National Center for Health Statistics reports
• Mean systolic blood pressure for males 35-44
  years of age is 128 and the standard deviation in
  this population is 15.
• The medical director of a large company looks at
  the records of 72 male executives in this age
  group and finds a mean of 126.07.
• Is this evidence that the company executives
  blood pressures are different from the general
  population?

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Executives Blood Pressures

• Assume the standard deviation for the company is
  the same as for the general population at 15

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Executives Blood Pressures

• Step 1
• Identify the population of interest and the
  parameter we want to draw conclusions about.

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Executives Blood Pressures

• Step 1
• State the null and alternative hypotheses
• in words
• and in symbols

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Executives Blood Pressures

• Step 2
• Choose the appropriate inference procedure.
• Verify the conditions for using the selected
  procedure.

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Executives Blood Pressures

• Step 3
• Carry out the inference procedure.
• Calculate the test statistic.
• Something new
• One-sample z-statistic
• Z x-bar µ0
• ?/vn

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Executives Blood Pressures

• Find the p-value.
• Sketch the distribution using z.
• In this example
• P-value 2P(z gt 1.09) 2(1-0.862) 0.2758
• Or
• 1 - ShadeNorm (-1.09,1.09,0,1.77)
• 2

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Executives Blood Pressure

• Step 4
• Interpret your results in the context of the
  problem.

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Executives Blood Pressure

• More than 27 of the time an SRS of size 72 from
  the general population would have a mean blood
  pressure at least as far from 128 as that of the
  company sample.

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Executives Blood Pressures

• We do not have strong enough evidence to reject
  the null hypothesis that our company executives
  are different from the general population.

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Can You Balance Your Checkbook?

• The average young person cant even balance a
  checkbook.

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Can You Balance Your Checkbook?

• The National Assessment for Educational Progress
  survey says that a score of 275 or higher on its
  quantitative test reflects the skill needed to
  balance a checkbook.

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Can You Balance Your Checkbook?

• An NAEP random sample of 840 young Americans had
  a mean score of 272.
• Is this sample result strong enough evidence to
  say that the mean for all young Americans is
  below 275?
• Assume ? 60.

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Can You Balance Your Checkbook?

• Step 1
• Population of interest
• Parameter of interest
• Null Hypothesis
• Alternative Hypothesis

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Can You Balance Your Checkbook?

• Step 2
• Choose the appropriate inference procedure.
• Verify the conditions for using the selected
  procedure.
• Random?
• Normal?

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Can You Balance Your Checkbook?

• Step 3
• If conditions are met, carry out the procedure
• Calculate the one-sample z-statistic.
• Find the p-value.

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Can You Balance Your Checkbook?

• Step 4
• Interpret your results in the context of the
  problem.

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Your Turn

• Textbook Page 576
• 10.40
• 10.79