Chi square

A phone battery manufacturer claims that his battery lives are approximately normally distributed with a standard deviation equal to 0.9 years. Suppose a random sample of 10 of these batteries has a standard deviation of 1.2 years. Do you think that the standard deviation is greater than 0.9 years? Use a 0.05 level of significance.

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} s_1=0.9 \\ {s}_2=1.2 \\ {n}_2=10 \\ \alpha =0.05 \\ T=16.919 \\ {\chi }^2>16.919 \\ {S}_2=s_2^2=1.2^2=\frac{36}{25}=1\frac{11}{25}=1.44 \\ {\chi }_2=(n_2-1)\cdot S_2/s_1^2=(10-1)\cdot 1.44/0.9^2=16 \\ {\chi }_2<T \\ x=0 \end{gathered}$$

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