A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals.
Using $\alpha$ = .01,observed chi-square value is ______________.
A) 24.93
B) 4.44
C) 32.89
D) 51.79
E) 54.98

Question

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals.  
Using $\alpha$ = .01,observed chi-square value is ______________.
A) 24.93 
B) 4.44 
C) 32.89 
D) 51.79 
E) 54.98

Quizplus · Accepted Answer

To find the observed chi-square value, we need to calculate the expected frequencies for each cell in the contingency table. To do this, we can use the formula:

Expected Frequency = (row total * column total) / grand total

For example, the expected frequency for the first cell in the table would be:

Expected Frequency = (45 * 120) / 300 = 18

Using this formula, we can calculate the expected frequencies for all 12 cells in the table. Once we have the expected frequencies, we can calculate the chi-square statistic using the formula:

chi-square = ∑ [(O-E)² / E]

where O is the observed frequency and E is the expected frequency.

After performing those calculations, we find that the observed chi-square value is 51.79. At a significance level of .01 with 2 degrees of freedom (since there are 2 categories of income and 4 categories of gasoline), the critical chi-square value is 9.21. Since the observed chi-square value is greater than the critical value, we reject the null hypothesis and conclude that there is a significant relationship between income level and grade of gasoline purchased.

A Gasoline Distributor Wonders Whether an Individual's Income Level Influences α\alphaα

A Gasoline Distributor Wonders Whether an Individual's Income Level Influences $\alpha$