A used car dealer claims that the median cost of a used car is $12,000. In a random sample of 15 used cars, you find that 8 of them have a price below $ 12,000 and that 4 of them have a price above $12,000. Test the claim of the used car dealer at the 5% significance level using the sign test.

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Asked Jun 19, 2019
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A used car dealer claims that the median cost of a used car is $12,000. In a random sample of 15 used cars, you find that 8 of them have a price below $ 12,000 and that 4 of them have a price above $12,000. Test the claim of the used car dealer at the 5% significance level using the sign test.

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Expert Answer

Step 1

Given median cost of a used car = $12000

Total number of used cars in sample = n = 15
Total number of used cars cost less than $12000 = 8
Total number of used cars cost greater than $12000 = 4

Here we run one sample Sign test for median
Null hypothesis H0 : η = η0
Alternative hypothesis Ha : η ≠ η0

 

Step 2

Test Statistic S = max{S1, S2} where S1, S2 are number of observations less than and greater than median cost of used car $12000 in the sample.
S1 = 8
S2 = 4

S = max {...

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p 2Pr[X2 S] X Binomial(n, -

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