Question

A newspaper article indicated that 43 percent of cars with black seats are white, 46 percent of cars with black seats are blue, 7 percent of cars with black seats are red, and 4 percent of cars with black seats are black. A test was conducted to investigate whether the color of cars with black seats was consistent with the newspaper article. A random sample of cars of these colors was selected, and the value of the chi-square test statistic was

Answer 1

Complete question :

A newspaper article indicated that 43 percent of cars with black seats are white, 46 percent of cars with black seats are blue, 7 percent of cars with black seats are red, and 4 percent of cars with black seats are black. A test was conducted to investigate whether the color of cars with black seats was consistent with the newspaper article. A random sample of cars of these colors was selected, and the value of the chi-square test statistic was x = 8.2. Which of the following represents the p-value for the test?

A) P(x2 ≥ 8.2) = 0.08

B) P(x2 ≥ 8.2) = 0.04

C) P(x2 ≤ 8.2) = 0.96

D) P (x2 = 8.2) = 0.00

E) The p-value cannot be calculated because the sample size is not given.

Answer:

P(χ² ≥ 8.2) = 0.04

Step-by-step explanation:

We need to obtain the degree of freedom ;

Number of levels, k - 1

k = (white, blue, red, black) = 4

df = k - 1= 4 - 1 = 3

The test statistic, χ² = 8.2

The Pvalue is the probability of a Chisquare statistic with 3 degree of freedom is equal to or more extreme than the statistic value, 8.2

Using the Pvalue for calculator from Chisquare statistic, at 3 degree of freedom

Pvalue(8.2, 3) = 0.042

Hence,

P(χ² ≥ 8.2) = 0.04