Question

Question 1 2 pts w The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877 teens (grades 7 to 12). One question asked was "What do you think are the chances you will be married in the next ten years?" Here is a two-way table of the responses by gender: Female 119 150 Male 103 Almost no chance Some chance, but probably not A 50-50 chance A good chance Almost certain 171 512 447 735 1174 710 756 Write a null and alternative hypothesis for conducting a chi-square test for independence in this scenario. HTML Editorial B 1 IC A - A - IE * 3 1 x x TT 12pt Paragraph Ho:

Answer 1

Observed Frequencies
	C1	C2	Total
R1	119	103	222
R2	150	171	321
R3	447	512	959
R4	735	710	1445
R5	1174	756	1930
Total	2625	2252	4877
Expected Frequencies
	C1	C2	Total
R1	2625 * 222 / 4877 = 119.4894	2252 * 222 / 4877 = 102.5106	222
R2	2625 * 321 / 4877 = 172.7753	2252 * 321 / 4877 = 148.2247	321
R3	2625 * 959 / 4877 = 516.1729	2252 * 959 / 4877 = 442.8271	959
R4	2625 * 1445 / 4877 = 777.7578	2252 * 1445 / 4877 = 667.2422	1445
R5	2625 * 1930 / 4877 = 1038.8046	2252 * 1930 / 4877 = 891.1954	1930
Total	2625	2252	4877
	(fo-fe)²/fe
R1	(119 - 119.4894)²/119.4894 = 0.002	(103 - 102.5106)²/102.5106 = 0.0023
R2	(150 - 172.7753)²/172.7753 = 3.0022	(171 - 148.2247)²/148.2247 = 3.4995
R3	(447 - 516.1729)²/516.1729 = 9.2699	(512 - 442.8271)²/442.8271 = 10.8053
R4	(735 - 777.7578)²/777.7578 = 2.3506	(710 - 667.2422)²/667.2422 = 2.74
R5	(1174 - 1038.8046)²/1038.8046 = 17.595	(756 - 891.1954)²/891.1954 = 20.5093

Null and Alternative hypothesis:

Ho: gender and response are independent.

H1: gender and response are dependent.

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Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 69.776

df = (r-1)(c-1) = 4

Critical value:

χ²α = CHISQ.INV.RT(0.05, 4) = 9.488

p-value:

p-value = CHISQ.DIST.RT(69.7763, 4) = 0