Question

A researcher tests whether homeownership (own, rent/other) is related to or independent of participants positive or negative views of the economy. The researcher records whether or not 105 participants own a home and whether their economic viewpoint is positive or negative. The following table lists the observed frequencies for this study. Conduct a chi-squared test for independence at a .05 level of significance. Decide whether to retain or reject the null hypothesis.

                                 Positive                                     Negative

Own                          35                                                  32                          67

Rent/Other                20                                                  18                         38

                                55                                                   50                        N=105

Answer 1

Claim: Homeownership (own, rent/other) is independent of participants positive or negative views of the economy.

The null and alternative hypothesis is

H0: Homeownership (own, rent/other) is independent of participants positive or negative views of the economy.

H1: Homeownership (own, rent/other) is not independent of participants positive or negative views of the economy.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

	Positive	Negative	Total
Own	35	32	67
Rent/Other	20	18	38
Total	55	50	105

O	E	(O-E)	(O-E)^2	(O-E)^2/E
35	35.09524	-0.09524	0.00907	0.000258
32	31.90476	0.095238	0.00907	0.000284
20	19.90476	0.095238	0.00907	0.000456
18	18.09524	-0.09524	0.00907	0.000501
			Total	0.0015

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 2 - 1) * (2 - 1) = 1 * 1 = 1

Critical value = 3.841

( From chi-square table)

Critical value > test statistic we fail to reject the null hypothesis.

Conclusion:

Homeownership (own, rent/other) is independent of participants positive or negative views of the economy.