Question

This question refers to a sweepstakes promotion in which respondents were asked to select what color car they would like to receive if they had the winning number. For a random sample of respondents the choices were 24 blue (B), 34 green(G), 66 red(R), and 36 white(W). Test at the 0.05 level the claim that the population prefers each colour equally. The expected value of chi-square (the test statistics) is

Select one:

a. 7.815

b. 24.600

c. 0

d. 22.412

e. 9.488

This question refers to a sweepstakes promotion in which respondents were asked to select what color car they would like to receive if they had the winning number. For a random sample of respondents the choices were 24 blue (B), 34 green(G), 66 red(R), and 36 white(W). Test at the 0.05 level the claim that the population prefers each colour equally. The critical value chi_square_c is

Select one:

a. 9.488

b. 24.600

c. 22.412

d. 0

e. 7.815

Answer 1

Solution:

Given:

claim: the population prefers each colour equally.

We have to find The expected value of chi-square (the test statistics).

Chi square test statistic for goodness of fit

Where

Oi = Observed Counts

Ei =Expected Counts = N / k = 160 / 4 = 40

Thus we need to make following table

Color	Oi	Ei	Oi^2/Ei
Blue	24	40	14.4
Green	34	40	28.9
Red	66	40	108.9
White	36	40	32.4
	160

Thus

Thus correct answer is:

b. 24.600

Part b) The critical value chi_square_c =.......?

df = k - 1= 4 - 1= 3

level of significance = 0.05

Chi-square critical value = 7.815