Answer to Question #152903 in Statistics and Probability for hadi

Question

2. Prior to the earthquake and tsunami tragedy in Japan, it was found that the price of imported used Toyota Estima were normally distributed with mean price of RM170,000. After the disaster that hit Japan many claimed that the mean price of imported used Toyota Estima had dropped sharply. Driven by curiosity and want to apply statistical knowledge, a group of students of the Faculty of Economics and Management (FEP) UKM conducted a survey at 25 used imported car shops and found that the average price of a Toyota Estima car is RM165,000 per unit with a standard deviation of RM15,000 . Has the claim of earthquake and tsunami disaster in Japan reduced the price of imported Toyota Estima cars? Test this claim with a significance level of 5%.

Answer 1

X denotes price of an imported used Toyota Estima car.

One sample t-test:

H₀: μ = 170000

H₁: μ < 170000

$t = \frac{\bar{x}-μ}{\frac{sd}{\sqrt{n}}} \\ n = 25 \\ \bar{x} = 165000 \\ μ = 170000 \\ sd = 15000 \\ t_{c} = \frac{165000 -170000}{\frac{15000}{\sqrt{25}}} = -1.666667$

Degrees of freedom $= n -1 = 24$

$p-value = P(t_{24} < -1.666667) = 0.05429003$

Level of significance α = 0.05

p-value > α

We cannot reject our null hypothesis.

There is no significant evidence that earthquake and tsunami disaster in Japan reduced the price of imported used Toyota Estima cars.