Question 869939
<font color="blue">Hypothesis:</font>



H0: mu = 2.1
H1: mu =/= 2.1 (mean mu is not equal to 2.1)



This is a two tailed test. So the p value will be visually represented as the area under the curve in both tails


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<font color="blue">Test Statistic:</font>



z = (xbar - mu)/(s/sqrt(n))



z = (2-2.1)/(0.29/sqrt(35))



z = -2.04002751141367



z = -2.04



The test statistic is -2.04



Since this value is negative, we are going to be finding the area under the curve to the left of this test statistic.


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<font color="blue">P value:</font>


Now use a <a href="http://www.math.upenn.edu/~chhays/zscoretable.pdf">table</a> to find that the area to the left of z = -2.04 is 0.0207



Double this to get 2*0.0207 = 0.0414 (remember, this is a two tailed test, so the area is symmetrical about the center mean making it in the tips of both tails)



The p value for this two tailed test, and test statistic, is 0.0414



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<font color="blue">Comparing the p value with alpha and making a decision:</font>



The p value is 0.0414
The significance level is alpha = 0.01 (note: 1% significance means alpha = 0.01)



The p value is larger than alpha since 0.0414 > 0.01. 
This means we fail to reject the null hypothesis H0. 
That makes us "accept" the null hypothesis and we must conclude that mu = 2.1



Interpretation: We conclude that the mean number of dogs owned by dog-owning households is 2.1 dogs (as stated initially in the problem, ie this test confirms it).