L12 & L13 Social Science Statistics

 Regarding Confidence Intervals for the mean of differences with dependent samples:

• Calculate and interpret a confidence interval for the mean of differences 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 for the confidence interval.

Regarding Hypothesis Testing for the mean of differences with dependent samples:

• 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:

• The key characteristic of dependent samples (or matched pairs) is that knowing which subjects will be in group 1 determines which subjects will be in group 2.

• We use slightly different variables when conducting inference using dependent samples:

  Group 1 values: x1
  1  Group 2 values: x2${\mathrm{<br>}}_{}$  Differences: d$\mathrm{<br>}$ Population mean: μd${\mathrm{<br>}}_{}$  Sample mean: d¯$\overline{�}$  Sample standard deviation: sd${\mathrm{<br>}}_{}$

• When conducting hypothesis tests using dependent samples, the null hypothesis is always 0μd=0
  , indicating that there is no change between the first population and the second population. The alternative hypothesis can be left-tailed (<$<$), right-tailed(>$>$), or two-tailed(≠$\ne$)

• 
  

By the end of Lesson 13:

Regarding Confidence Intervals for difference of two means of independent samples:

• Calculate and interpret a confidence interval given a confidence level and a given parameter.

Point estimate is mean 1 - mean 2.

• 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 for the confidence interval.

    >You can conduct a hypothesis test on a slightly skewed hystogram as long as there aren't any large outliers.

Regarding Hypothesis Testing for difference of two means of independent samples:

• 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