# Test statistics #### All in One Place

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##### Intros
###### Lessons
1. The Test Statistic is a Z-score corresponding to a particular Null Hypothesis. It is given below for the two types of claims:

• Proportion:
$Z= \frac{ \hat{p}-p}{ \sqrt{{ \frac{p(1-p)}{n}}}}$

• Mean:
$Z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$
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##### Examples
###### Lessons
1. Charlie goes to a thrift store and tries on 50 Hawaiian shirts. He finds that he likes 35 of them. If Charlie were to try on every Hawaiian shirt in the store what is the test statistic that he likes;
1. 60% of all the Hawaiian Shirts?
2. 70% of all the Hawaiian Shirts?
3. 80% of all the Hawaiian Shirts?
2. From a batch of 100 Toblerone Bars, the mean weight was found to be $\overline{x} =170$g. It is known that the standard deviation of all Toblerone bars is $\sigma=15$g. Find the test statistic that the mean weight of all Toblerone bars is,
1. $\mu=165$g
2. $\mu=170$g
3. $\mu=175$g