Answer to Question #152904 in Statistics and Probability for hadi

Question

3. The Ministry of International Trade and Industry would also like to see the impact of the earthquake and tsunami disaster that hit Japan on the average price of imported Toyota Estima cars. A ministry expert said that if it was found that more than 30% of used car dealers had lowered prices, then a strong conclusion could be drawn that there would be a significant impact on the decline in Toyota Estima car prices due to the disaster in Japan. Out of 200 samples of used car dealers it was found that only 50 had lowered the price and the rest did not. Test whether the price of imported Toyota Estima cars has decreased using 95% confidence level

Answer 1

$\hat{p}=50/200=0.25$

z Test for a Proportion:

H₀: p=0.3

H₁: p<0.3

Finding critical value for $\alpha=0.05$ (left-tailed test)

critical value = -1.645

Computing the test value:

$z=\frac{\hat{p}-p}{\sqrt{p(1-p)/n}}=\frac{0.25-0.3}{\sqrt{0.3*0.7/200}}=-1.543$

Since critical value<z, we can't reject null hypothesis.

There is not enough evidence to reject the claim that the price of imported Toyota Estima cars has decreased.