L9 Social Science Statistics

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

  • Conduct a Hypothesis Test for a single mean with σ known:
    • State the null hypothesis (Ho)= the claim or status quo
    • and alternative hypothesis (Ha)= what we are trying to prove or find evidence for

    • Calculate the test-statistic 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 this hypothesis test.
    • Draw a correct conclusion for the hypothesis test.
    • Interpret a Type I and II error.
  • ART= rejecting null hypothesis when it is true (A comes before B so Type 1 error)
  • BFF= failing to reject Ho when it is false (B comes after A so Type 2 error)
  • Since Type 1 and Type 2 errors are on opposite ends of the spectrum, if you decrease the probability of one error, it will increase the probability of the other.
  • We choose the significance level based on the seriousness of making either error.


*P value is the evidence, it is the probability of getting your sample result if the hypothesis is true.

*P value is the probability of getting a test statistic (z-score) that is as extreme or more extreme than the one we got, if the null hypothesis is true.

*P value tells us how much evidence we have against Ho and in favor of Ha.

*The smaller the p value, the greater the chance against the null hypothesis.

    >How small is too small?.......significance level ( α)= the decision point for the p-value

    >( α) is chosen before collecting data. Common significance levels are .01, .05, .10

  • The level of significance (�) controls the probability of committing a Type I Error. 

REMEMBER:

>If P is low, Ho must go

>If P is high, keep the guy!

*Hypothesis are always written about parameters and never about statistics.

-NEVER say Ho is true. (Just say that you fail to reject)

*Alternative Hypothesis NEVER has the =.

    we label the null hypothesis 

0. The zero in the subscript represents “null,” “baseline,” “default,” “no effect,” etc. Similarly, we label the alternative hypothesis.

Our alternative hypothesis could have been written as:

  • ≠98.6 (two-sided hypothesis; two-tailed) *Shade left and right sections in aplet.
  • <98.6 (one-sided hypothesis; left-tailed)
  • >98.6 (one-sided hypothesis; right-tailed)

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