Question

10. A researcher claims that the mean rate of individuals below poverty in the City of Chicago is below 17 %. Based on the data represented for the years 2005 – 2011, perform a hypothesis test to test his claim using a significance level of α = 0.10.

11. Would your conclusion change for question 10 if you used a significance level of α = 0.05? Explain.

12. A survey conducted at Chicago Public Schools (CPS) involving high school students on whether they had participated in binged drinking during the past month. Binge drinking was defined as 5 or more drinks in a row on one or more of the past 30 days.

Number who identified as having participated in Binge Drinking.	72
Total participants	567

a. From the sample data is there evidence that the proportion of students who participate in binge drinking is greater than 10%? Write a null and alternative hypothesis and perform an appropriate significance test using α=0.05.

b. Construct a 90% Confidence Interval for the population proportion. Does it support the same conclusion as in 12a? Explain.

Community Area	Community Area Name	Below Poverty Level	Crowded Housing	Dependency	No High School Diploma	Per Capita Income	Unemployment
1	Rogers Park	22.7	7.9	28.8	18.1	23714	7.5
2	West Ridge	15.1	7	38.3	19.6	21375	7.9
3	Uptown	22.7	4.6	22.2	13.6	32355	7.7
4	Lincoln Square	9.5	3.1	25.6	12.5	35503	6.8
5	North Center	7.1	0.2	25.5	5.4	51615	4.5
6	Lake View	10.5	1.2	16.5	2.9	58227	4.7
7	Lincoln Park	11.8	0.6	20.4	4.3	71403	4.5
8	Near North Side	13.4	2	23.3	3.4	87163	5.2
9	Edison Park	5.1	0.6	36.6	8.5	38337	7.4
10	Norwood Park	5.9	2.3	40.6	13.5	31659	7.3
11	Jefferson Park	6.4	1.9	34.4	13.5	27280	9
12	Forest Glen	6.1	1.3	40.6	6.3	41509	5.5
13	North Park	12.4	3.8	39.7	18.2	24941	7.5
14	Albany Park	17.1	11.2	32.1	34.9	20355	9
15	Portage Park	12.3	4.4	34.6	18.7	23617	10.6
16	Irving Park	10.8	5.6	31.6	22	26713	10.3
17	Dunning	8.3	4.8	34.9	18	26347	8.6
18	Montclaire	12.8	5.8	35	28.4	21257	10.8
19	Belmont Cragin	18.6	10	36.9	37	15246	11.5
20	Hermosa	19.1	8.4	36.3	41.9	15411	12.9
21	Avondale	14.6	5.8	30.4	25.7	20489	9.3
22	Logan Square	17.2	3.2	26.7	18.5	29026	7.5
23	Humboldt Park	32.6	11.2	38.3	36.8	13391	12.3
24	West Town	15.7	2	22.9	13.4	39596	6
25	Austin	27	5.7	39	25	15920	21
26	West Garfield Park	40.3	8.9	42.5	26.2	10951	25.2
27	East Garfield Park	39.7	7.5	43.2	26.2	13596	16.4
28	Near West Side	21.6	3.8	22.9	11.2	41488	10.7
29	North Lawndale	38.6	7.2	40.9	30.4	12548	18.5
30	South Lawndale	28.1	17.6	33.1	58.7	10697	11.5
31	Lower West Side	27.2	10.4	35.2	44.3	15467	13
32	Loop	11.1	2	15.5	3.4	67699	4.2
33	Near South Side	11.1	1.4	21	7.1	60593	5.7
34	Armour Square	35.8	5.9	37.9	37.5	16942	11.6
35	Douglas	26.1	1.6	31	16.9	23098	16.7
36	Oakland	38.1	3.5	40.5	17.6	19312	26.6
37	Fuller Park	55.5	4.5	38.2	33.7	9016	40
38	Grand Boulevard	28.3	2.7	41.7	19.4	22056	20.6
39	Kenwood	23.1	2.3	34.2	10.8	37519	11
40	Washington Park	39.1	4.9	40.9	28.3	13087	23.2
41	Hyde Park	18.2	2.5	26.7	5.3	39243	6.9
42	Woodlawn	28.3	1.8	37.6	17.9	18928	17.3
43	South Shore	31.5	2.9	37.6	14.9	18366	17.7
44	Chatham	25.3	2.2	40	13.7	20320	19
45	Avalon Park	16.7	0.6	41.9	13.3	23495	16.6
46	South Chicago	28	5.9	43.1	28.2	15393	17.7
47	Burnside	22.5	5.5	40.4	18.6	13756	23.4
48	Calumet Heights	12	1.8	42.3	11.2	28977	17.2
49	Roseland	19.5	3.1	40.9	17.4	17974	17.8
50	Pullman	20.1	1.4	42	15.6	19007	21
51	South Deering	24.5	6	41.4	21.9	15506	11.8
52	East Side	18.7	8.3	42.5	35.5	15347	14.5
53	West Pullman	24.3	3.3	42.2	22.6	16228	17
54	Riverdale	61.4	5.1	50.2	24.6	8535	26.4
55	Hegewisch	12.1	4.4	41.6	17.9	22561	9.6
56	Garfield Ridge	9	2.6	39.5	19.4	24684	8.1
57	Archer Heights	13	8.5	40.5	36.4	16145	14.2
58	Brighton Park	23	13.2	39.8	48.2	13138	11.2
59	McKinley Park	16.1	6.9	33.7	31.8	17577	11.9
60	Bridgeport	17.3	4.8	32.3	25.6	24969	11.2
61	New City	30.6	12.2	42	42.4	12524	17.4
62	West Elsdon	9.8	8.7	38.7	39.6	16938	13.5
63	Gage Park	20.8	17.4	40.4	54.1	12014	14
64	Clearing	5.9	3.4	36.4	18.5	23920	9.6
65	West Lawn	15.3	6.8	41.9	33.4	15898	7.8
66	Chicago Lawn	22.2	6.5	40	31.6	14405	11.9
67	West Englewood	32.3	6.9	40.9	30.3	10559	34.7
68	Englewood	42.2	4.8	43.4	29.4	11993	21.3
69	Greater Grand Crossing	25.6	4.2	42.9	17.9	17213	18.9
70	Ashburn	9.5	4.2	36.7	18.3	22078	8.8
71	Auburn Gresham	24.5	4.1	42.1	19.5	16022	24.2
72	Beverly	5.2	0.7	38.7	5.1	40107	7.8
73	Washington Heights	15.7	1.1	42.4	15.6	19709	18.3
74	Mount Greenwood	3.1	1.1	37	4.5	34221	6.9
75	Morgan Park	13.7	0.8	39.4	10.9	26185	14.9
76	O'Hare	9.5	1.9	26.5	11	29402	4.7
77	Edgewater	16.6	3.9	23.4	9	33364	9

Answer 1

Note : Allowed to solve only one question per post.

10. A researcher claims that the mean rate of individuals below poverty in the City of Chicago is below 17 %. Based on the data represented for the years 2005 – 2011, perform a hypothesis test to test his claim using a significance level of α = 0.10.

Step1 : Put the data in excel and find the mean and standard deviation of the variable Below poverty level.

Step 2 : Hypothesis testing

Ho: the mean poverty level is equal to 17%
H1: the mean poverty level is less than 17%

Hence there is no sufficient evidence to support the claim that the mean rate of individuals below poverty in the City of Chicago is below 17 %

11. Would your conclusion change for question 10 if you used a significance level of α = 0.05? Explain.

No the conclusion will change. The pvalue for the test is 0.99 which is greater than 0.05, hence we fail to reject the null hypothesis and conclude that the the mean poverty level is equal to 17%