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Problem 2-2, Comparing a single mean to a specified value (second example)
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===Section A: Choosing hypotheses=== In this problem we are told we would like our liquid detergent to have a mean of <math>\mu_0 = 800</math> and a standard deviation of <math>\sigma = 25</math>: this is our theoretical distribution. We are also told that a sample of <math>N = 16</math> batches of detergent have an average viscosity of <math>\overline{y} = 812</math>, which estimates the mean of our true distribution. We would like to know if the means of our true and theoretical distributions are likely to be the same. There are two hypotheses to consider here. Our null hypothesis is that the means of the two distributions are equal, and our alternative hypothesis is that they are not equal. <center>H<sub>0</sub>: μ = μ<sub>0</sub><br /> H<sub>1</sub>: μ ≠ μ<sub>0</sub></center> The alternate hypothesis is called ''two-tailed'' because it is true if <math>\mu < \mu_0</math> and if <math>\mu > \mu_0</math>. <br clear='all'> [[Image:2-2fig2.png|thumb|left|'''Figure 2:''' Our plot after normalizing.]]
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