L10 & L11 Social Science Statistics

 By the end of lesson 10, you should be able to:

  • Calculate and interpret a confidence interval for a population mean given a confidence level.
  • Explain how the margin of error changes with the sample size and the level of confidence.
  • Identify a point estimate and margin of error for the confidence interval.
  • Show the appropriate connections between the numerical and graphical summaries that support this confidence interval.
  • Check the requirements of the confidence interval.
  • Calculate a desired sample size given a level of confidence and margin of error.

REMEMBER:

>Margin of error is (z* times sigma)/ square root of n). Ideally it is small.

> To reduce the margin of error: 
  • reduce sigma.
  • increase sample size (n)
  • decrease confidence level (which will reduce z*)
*A confidence interval does NOT tell us:
  • individual values
  • sample means
  • future samples (AVOID words like probability and chance)

L11

Regarding Confidence Intervals for a single mean with  unknown:

  • Calculate and interpret a confidence interval for a population mean given a confidence level.
  • Identify a point estimate and margin of error for the confidence interval.
  • Show the appropriate connections between the numerical and graphical summaries that support the confidence interval.
  • Check the requirements the confidence interval.

Regarding Hypothesis Testing for a single mean with  unknown:

  • State the null and alternative hypothesis.
  • Calculate the test-statistic, degrees of freedom and p-value of the hypothesis test.
  • Assess the statistical significance by comparing the p-value to the α-level.
  • Check the requirements for the hypothesis test.
  • Show the appropriate connections between the numerical and graphical summaries that support the hypothesis test.
  • Draw a correct conclusion for the hypothesis test.

REMEMBER:

  • df = n-1
  • The greater the degrees of freedom, the closer the t- distribution will look to a normal distribution.
  • When we use s instead of sigma for one mean, we call the result the standard error.
  • standard error= st. dev divided by square root of n.

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