Answer to Question #204849 in Calculus for jessy

Question

a school administrator claims that less than 50% of the students of the school are dissatisfied by the community cafeteria service. Test this claim by using sample data obtained from a survey of 500 students of the school where 54% indicated their dissatisfaction of the community cafeteria service. use a 0.05.

Answer 1

Answer:-

P: Population proportion dissatisfied by the community cafeteria service .

H_O: P =0.5

H₁=P<0.5

$\hat{P}:$ Sample proportion dissatisfied by community cafeteria service

$\hat{P}=0.54$

$Z=\frac{\hat{P}-P}{\sqrt{\hat{P}(1-\hat{P})\over n}}$ ~ N(0,1)

$Z=\frac{0.54-0.5}{\sqrt{(0.54)(0.46)}\over 500}$ $\implies$ $\frac{0.04}{0.022}$

$Z=1.82$

Level of significance $\alpha=0.05$

$Z_{\alpha}$ (onetail)=1.64

$Z>Z_{\alpha}$ at 5% level of significance , thus H_o will be rejected.

Hence school administer claim of $(P<0.5)$ will be accepted.