Performance comparing

A standardized test was administered to thousands of students with a mean score of 85 and a standard deviation of 8. A random sample of 50 students was given the same test and showed an average score of 83.20. Is there evidence that this group performs less than the ones in general at a 0.05 level?

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} m=85 \\ s=8 \\ {n}_2=50 \\ {m}_2=83.20 \\ \alpha =0.05 \\ Z=N(0,1) \\ z=\frac{m_2-m}{s/\sqrt{n_2}}=\frac{83.2-85}{8/\sqrt{50}}\doteq -1.591 \\ p=P(Z<z) \\ p=0.0559 \\ \alpha <p \\ x=0 \end{gathered}$$

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