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 were given the same test and showed an average score of 83.20. Is there evidence to show that this group has a lower performance than the ones in general at 0.05 level?

Result

x=

Yes

No

Step-by-step explanation:

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

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Showing 1 comment:

Miro

For p value we use our normal distribution calcuator:

https://www.hackmath.net/en/calculator/normal-distribution?mean=0&sd=1&above=-1&area=below&below=-1.591&ll=&ul=&outsideLL=&outsideUL=&draw=Calculate

17 days ago  Like

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