A study was performed to examine whether the type of gasoline used is independent of a...

A study was performed to examine whether the type of gasoline used is independent of a person's living status. The researcher surveyed 600 people and asked two questions. The first question asked was “Do you use regular, plus, or super gasoline when filling up?” The second question asked was “Do you rent or own your place of residence?” The results are shown below. Assume the significance level α = .05 is used for the test.

Type of Gas

Living Status	Regular	Plus	Super
Rent	173	68	49
Own	154	87	69

Under the null hypothesis, the expected number of people to rent and use regular gasoline is 158.05 and the expected number of people to own and use plus gasoline is 80.08. The numerical value of the chi-square test statistic is:

Solutions

Expert Solution

Observed Frequencies
	Regular	Plus	Super	Total
Rent	173	68	49	290
Own	154	87	69	310
Total	327	155	118	600
Expected Frequencies
	Regular	Plus	Super	Total
Rent	327 * 290 / 600 = 158.05	155 * 290 / 600 = 74.9167	118 * 290 / 600 = 57.0333	290
Own	327 * 310 / 600 = 168.95	155 * 310 / 600 = 80.0833	118 * 310 / 600 = 60.9667	310
Total	327	155	118	600
	(fo-fe)²/fe
Rent	(173 - 158.05)²/158.05 = 1.4141	(68 - 74.9167)²/74.9167 = 0.6386	(49 - 57.0333)²/57.0333 = 1.1315
Own	(154 - 168.95)²/168.95 = 1.3229	(87 - 80.0833)²/80.0833 = 0.5974	(69 - 60.9667)²/60.9667 = 1.0585

Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 6.1630

orchestra answered 2 years ago

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