Tests of Significance 2/4 & 2/5. Chapter 10. 10.10&12. Warm Up. Review your homework, ONLY #1,6,13, and see if you have an questions. . Questions about #1,6, & 13. Use a confidence interval when your goal is to estimate a population parameter
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Use a confidence interval when your goal is to estimate a population parameter
Use a Test of Significance to assess the evidence provided by data about some claim concerning a population.Tests of Significance
I make 80% of my free throws in basketball. You don’t believe me and want to test my claim. You make me shoot 20 free throws and I only make 8 out of 20.
The null hypothesis is the statement being tested in a test of significance.
Describe the effect you are searching for in terms of a population parameter
Step 1: Identify the population of interest and the parameter you want to draw conclusions about. State the null and alternative hypotheses in words and symbols.
Step 2: Choose the appropriate inference procedure. Verify the conditions for using the selected procedure.
SRS from population of interest
Sampling distribution is approx. normal.
Step 3: If the conditions are met, carry out the inference procedure.
Calculate the test statistic Find the P-value
Step 4: Interpret your results in the context of the problem.Inference Toolbox: Significance Tests
Diet colas use artificial sweeteners, and these sweeteners lose their sweetness over time. The manufacturer tests the sweetness of a diet cola after simulating four months of storage at room temperature. The trained testers rate the diet cola on a sweetness score from 1 – 10.
We want to know if the colas really do lose their sweetness.
Let’s walk through the steps of a test of significance together.Sweetening Colas
To test from an SRS of size n with unknown and known compute the one-sample z statistic:
isz Test for a population mean
Hence, if is true, and the mean sweetness loss for this cola is 0, there is about a 17% chance that we will obtain a sample of 10 sweetness loss values whose mean is 0.3 or greater.
This can happen by chance, easily.
Not strong evidence against the null hypothesis.One-sided P-value
If our alternative hypothesis is two-sided we will find a two-sided P-value.
Step 1: The population of interest is the pills and the parameter we want to draw conclusions about is the mean hardness. The null hypothesis is that the mean hardness is equal to 11.5 while the alternative hypothesis is that the mean hardness is not equal to 11.5