A professor

A professor in a typing class found out that the average performance of an expert typist is 85 words per minute. A random sample of 16 students took the typing test and an average speed of 62 words per minute was obtained with a standard deviation of 8. Can we say that the sample students performance is below the standard deviation at the 0.05 level of significance.

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} m=85 \\ s=8 \\ {n}_2=16 \\ {m}_2=83.20 \\ \alpha =0.05 \\ Z=N(0,1) \\ z={\displaystyle \frac{m_2-m}{s\mathrm{/}\sqrt{n_2}}}={\displaystyle \frac{83.2-85}{8\mathrm{/}\sqrt{16}}}=-{\displaystyle \frac{9}{10}}=-0.9 \\ p=P(Z<z) \\ p=0.0559 \\ \alpha <p \\ x=0=0 \end{gathered}$$

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