Question

2. In 2001, the U.S. Senate voted on the question of whether to allow oil and gas drilling in the Gulf of Mexico. The relationship between party affiliation and vote is shown in the following table:

allow drilling	democrat	republican	total
yes	18	49	67
no	33	0	33
total	51	49	100

A. Calculate chi-square for this table. Show your work. Draw a table just like the one above, leaving room in each cell to record these numbers: observed frequency (f0), expected frequency (fe), f0-fe, (f0-fe)2, and (f0-fe)2/fe.

B. Use chi-square to test the null hypothesis that, in the population from which the sample was drawn, there is no relationship between party and vote. Using Table 7-7, find the appropriate critical value (use the .05 level of significance). (i) Write down the critical value. (ii) Should you reject the null hypothesis or not reject the null hypothesis? (iii) Explain your reasoning.

C. Calculate lambda for this table. (i) Show your work. (ii) Write a sentence explaining exactly what the value of lambda means. (iii) State whether the relationship is weak, moderate, moderately strong, or strong.

Answer 1

f0	fe	f0-fe	(f0-fe)^2	(f0-fe)^2/fe
18	34.17	-16.17	261.4689	7.652002
49	32.83	16.17	261.4689	7.964328
33	16.83	16.17	261.4689	15.53588
0	16.17	-16.17	261.4689	16.17

• Ei is calculated as respective cell's row total multiplied by column total divided by the overall total.

  chi-square test statistic =sum((Oi-Ei)^2/Ei), which is equal to 47.32

• b)

=47.32

• i) Critical value for 1 degrees of freedom [(r-1)*(c-1)=1, where r=no. of rows and c=no. of columns] and 0.05 level of significance is 3.84

  ii) We reject the null hypothesis at 5% level of significance.

  iii) Since the value of test statistic (47.32) is greater than critical value (3.84), we should reject the null hypothesis and conclude that there is a relationship between party and vote.