Introduction to Inference Tests of Significance. Wording of conclusion revisit If I believe the statistic is just too extreme and unusual (P-value < 

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Presentation transcript:

Introduction to Inference Tests of Significance

Wording of conclusion revisit If I believe the statistic is just too extreme and unusual (P-value <  ), I will reject the null hypothesis. If I believe the statistic is just normal chance variation (P-value >  ), I will fail to reject the null hypothesis. We reject fail to reject H o, since the p-value< , there is p-value> , there is not enough evidence to believe…(H a in context…)

Example 3 test of significance  = true mean distance H o :  = 340 H a :  > 340 Given random sample Given normally distributed. Safe to infer a population of at least 100 missiles. We fail to reject H o. Since p-value>  there is not enough evidence to believe the mean distance traveled is more than 340 miles.

Familiar transition What happened on day 2 of confidence intervals involving mean and standard deviation? Switch from using z-scores to using the t- distribution. What changes occur in the write up?

Example 3 test of significance  = true mean distance H o :  = 340 H a :  > 340 Given random sample. Given normally distributed. Safe to infer a population of at least 100 missiles. We fail to reject H o. Since p-value>  there is not enough evidence to believe the mean distance traveled is more than 340 miles.

Example 3 t-test  = true mean distance H o :  = 340 H a :  > 340 Given random sample. Given normally distributed. Safe to infer a population of at least 100 missiles. We fail to reject H o. Since p-value>  there is not enough evidence to believe the mean distance traveled is more than 340 miles.

Example 3 t-test  = true mean distance H o :  = 340 H a :  > 340 Given random sample Given normally distributed. Safe to infer a population of at least 100 missiles. We fail to reject H o. Since p-value>  there is not enough evidence to believe the mean distance traveled is more than 340 miles.

Example 3 t-test  = true mean distance H o :  = 340 H a :  > 340 Given random sample. Given normally distributed. Safe to infer a population of at least 100 missiles. We fail to reject H o. Since p-value>  there is not enough evidence to believe the mean distance traveled is more than 340 miles.

t-chart

Example 3 t-test  = true mean distance H o :  = 340 H a :  > 340 Given random sample. Given normally distributed. Safe to infer a population of at least 100 missiles. We fail to reject H o. Since p-value>  there is not enough evidence to believe the mean distance traveled is more than 340 miles.

Example 3 t-test  = true mean distance H o :  = 340 H a :  > 340 Given random sample. Given normally distributed. Safe to infer a population of at least 100 missiles. We fail to reject H o. Since p-value>  there is not enough evidence to believe the mean distance traveled is more than 340 miles.

1 proportion z-test p = true proportion pure short H o : p =.25 H a : p =.25 Given a random sample. np = 1064(.25) > 10 n(1–p) = 1064(1–.25) > 10 Sample size is large enough to use normality Safe to infer a population of at least 10,640 plants. We fail to reject H o. Since p-value>  there is not enough evidence to believe the proportion of pure short is different than 25%.