Question

The popularity of computer, video, online, and virtual reality games has raised concerns about their ability to negatively impact youth. The data in this exercise are based on a recent survey of 14- to 18-year-olds in Connecticut high schools. Here are the grade distributions of boys who have and have not played video games.

	Grade average
	A's and B's	C's	D's and F's
Played games	737	449	194
Never played games	204	143	79

The null hypothesis "no relationship" says that in the population of all 14- to 18- year-old boys in Connecticut, the proportions who have each grade average are the same for those who play and don't play video games.

(a) Find the expected cell counts if this hypothesis is true, and display them in a two-way table. Check that the row and column totals agree with the totals for the observed counts. (Round your answers to two decimal places.)

	A's and B's	C's	D's and F's
Played games
Never played games

Answer 1

Null and Alternate Hypothesis

H₀: The two variables (Games Played and Grade Average) are independent.

H_a: The two variables are associated.

Given,

Observed Values:

Expected Values:

Expected Values are calculated as:

E_ij = (T_i * T_j)/N

where,

T_i = Total in ith row

T_j = Total in jth column

N = table grand total

Alpha = 0.05

df = (r-1)*(c-1) = (2-1)*(3-1) = 1*2 = 2

Chi Square _Critical = 5.99

Decision Rule:

If Chi Square> Chi Square _Critical reject the null hypothesis

Test Statistic:

Chi Square = ∑(O_ij – E_ij)²/E_ij = (737-719.04)²/719.04 + ……………….. + (79 – 64.4)²/64.4 = 6.34

Result:

Since, Chi Square> Chi Square _Critical we reject the null hypothesis.

Conclusion:

Playing Games and Grade Average are associated