Question

Background: Morris Saldov conducted a study in Eastern and Central Newfoundland in 1988 to examine public attitudes towards social spending. In particular, the study tried to determine if knowing someone on public assistance (yes, no) affected one's views on social spending (too little, about right, too much). The data from the study is summarized in the table below.

	Yes	No	Total
Too little	39	8	47
About right	15	15	30
Too much	9	9	18
Total	63	32	95

Source: Morris Saldov, Public Attitudes to Social Spending in Newfoundland," Canadian Review of Social Policy, 26, November 1990, pages 10-14.

Directions: Conduct a chi-square test for independence to determine if the association between knowing someone on public assistance and views on social spending is statistically significant.

1. Choose the correct null and alternative hypotheses.
   • H0:H0: There is an association between knowing someone on public assistance and views on social spending.
     HaHa There is no association between knowing someone on public assistance and views on social spending.
   • H0:H0: There is no association between knowing someone on public assistance and views on social spending.
     HaHa There is an association between knowing someone on public assistance and views on social spending.
2. Compute the test statistic.
   
   Complete the following table of expected counts. (Round your answers to 2 decimal places).
   

   	Yes	No
   Too little
   About right
   Too much

   
   Compute the value of the test statistic. (Round your answer to 2 decimal places.)
   
   χ2=χ2=
   
3. Compute the p-value. (Round your answer to 4 decimal places.)
   
   pp-value =  
   
4. Interpret the results of the significance test. Use a signifcance level of alpha = 0.05 (choose one)
   • The p-value provides little evidence against the null hypothesis. The association between knowing someone on public assistance and attitudes towards social spending is not statistically significant.
   • The p-value provides strong evidence against the null hypothesis. The association between knowing someone on public assistance and attitudes towards social spending is statistically significant.

Answer 1

(a)

Correct option:

H0: There is no association between knowing someone on public assistance and views on social spending.
Ha There is an association between knowing someone on public assistance and views on social spending.

(b)

Expected counts Table is completed as follows:

	Yes	No
Too little
About right
Too much

(c)

The value of the test statistic. is got as follows:

Observed (O)	Expected (E)	(O - E)2/E
39	31.17	1.97
8	15.83	3.87
15	19.89	1.20
15	10.11	2.37
9	11.94	0.72
9	6.06	1.42
Total = =		11.56

So,

The value of the test statistic = = 11.56

(d)

ndf = (r - 1) X (c - 1)

= (3 - 1) X (2 - 1)

= 2

By Technology, p - value = 0.0031

Correct option:

The p-value provides strong evidence against the null hypothesis. The association between knowing someone on public assistance and attitudes towards social spending is statistically significant.