Topic: Hypothesis tests on one proportion

Using the demographics data, test if the population is increasing in half of US counties at the 10% significance level.

County	State	2017 Population	Population Increasing	Poverty Percentage	Homeownership Percentage	Multi Unit Family Percentage	Unemployment Percentage	Metro	Median Household Income
Coffee County	Alabama	51874	1	16.1	69.7	13.6	4.39	0	49821
Covington County	Alabama	37092	0	17.6	74	6.1	5.24	0	39467
Dallas County	Alabama	39215	0	31.9	62.6	16	7.53	0	30065
Valdez-Cordova Census Area	Alaska	9278	0	7.4	71.8	17.6	7.96	0	86019
St. Francis County	Arkansas	25930	0	27.5	58.7	15.2	5.08	0	33102
Van Buren County	Arkansas	16506	0	19.6	78.5	9.9	5.42	0	34428
Alameda County	California	1663190	1	11.3	55.1	38	3.64	1	85743
El Dorado County	California	188987	1	9.8	76.5	12.1	4.36	1	74885
Fresno County	California	989255	1	25.4	55	25.8	8.47	1	48730
Kern County	California	893119	1	22.6	61.4	18.1	9.21	1	50826
Los Angeles County	California	10163507	1	17	48.2	41.8	4.69	1	61015
Tuolumne County	California	54248	1	13.6	70.2	8.6	5.39	0	54325
Yuba County	California	77031	1	18.5	59.8	17.8	7.44	1	51776
Montezuma County	Colorado	26140	1	16.8	72.8	9.5	4	0	45645
Morgan County	Colorado	28192	1	9.3	67.3	12.1	2.44	0	51456
San Miguel County	Colorado	7967	1	10.5	64.3	40	2.85	0	62243
Alachua County	Florida	266944	1	23.3	54.9	38	3.7	1	45478
Jenkins County	Georgia	8767	0	30.7	75.8	2.1	6.83	0	27197
Montgomery County	Georgia	9031	1	19.5	71.3	6.7	6.64	0	40308
Newton County	Georgia	108078	1	16.7	76	8.7	5.32	1	52784
Crawford County	Illinois	18961	0	11.9	80.4	9.5	5.18	0	47468
Gallatin County	Illinois	5080	0	16.6	79	7.3	5.66	0	42450
Schuyler County	Illinois	7035	0	21.5	78.8	5.8	4.41	0	47321
Benton County	Indiana	8613	0	14.9	78.7	8	3.39	1	49183
LaPorte County	Indiana	110029	0	16.6	75.4	16.5	4.47	1	49921
Montgomery County	Indiana	38525	1	10.2	73.6	15.6	3.03	0	53075
Perry County	Indiana	19081	0	14.5	78.2	9.3	3.81	0	49689
Lee County	Iowa	34295	0	16.3	74.1	15.7	5.51	0	48266
Ringgold County	Iowa	5034	1	10.9	79.2	6.7	3.08	0	50642
Warren County	Iowa	50163	1	6.2	79.1	14.2	2.75	1	71514
Barton County	Kansas	26476	0	15.7	74.1	8.1	3.62	0	46070
Doniphan County	Kansas	7727	0	13.7	75.2	6.9	3.46	1	50300
Morris County	Kansas	5455	0	9.8	77.6	7.4	3.12	0	50338
Wilson County	Kansas	8675	0	16.8	76.2	8.6	4.7	0	44468
Boyle County	Kentucky	29924	1	15.5	69	18.9	5.02	0	43076
Carter County	Kentucky	27144	0	21.5	77.9	5.5	9.57	0	35095
Montgomery County	Kentucky	27928	1	23	68.7	13.9	6.57	0	42172
Tensas Parish	Louisiana	4615	0	38	60.1	3.6	8.4	0	21906
Lincoln County	Maine	34204	1	11.8	85.7	6.5	3.23	0	54041
Washington County	Maine	31593	0	18.2	76.2	8	4.91	0	40328
Charles County	Maryland	159700	1	6.9	81.1	9.8	3.99	1	93973
Kent County	Maryland	19384	0	13.1	71.8	12.6	4.48	0	56638
Midland County	Michigan	83411	0	11.3	76.6	14.8	4.75	1	57117
Houston County	Minnesota	18660	0	8.9	81.7	11.2	3.38	1	56837
Wilkin County	Minnesota	6324	0	9.9	83	13.4	3.13	0	52917
Carroll County	Mississippi	10139	0	14	81.4	3.2	5.81	0	43068
Tishomingo County	Mississippi	19542	1	18.6	79.8	6.1	5	0	36672
Cedar County	Missouri	14073	1	22.6	76.3	5.6	4.11	0	35930
Morgan County	Missouri	20145	1	25.5	81.7	3.5	5	0	34776
Perry County	Missouri	19225	1	8.2	78.1	7.3	2.7	0	54935
Phelps County	Missouri	44744	0	20.4	65.5	19.2	3.81	0	41681
Platte County	Missouri	101187	1	7.2	67.7	27.1	3.18	1	74199
Wayne County	Missouri	13296	0	23.4	73.3	4.2	5.13	0	35135
Golden Valley County	Montana	822	0	18.2	76	0	5	1	43854
Treasure County	Montana	679	0	17	67.7	0.7	3.77	0	42454
Boone County	Nebraska	5352	0	7.3	74.6	7.1	2.47	0	53854
Hayes County	Nebraska	893	0	9	70.2	2.3	2.46	0	44946
Elko County	Nevada	52649	1	11.5	71.1	15.9	3.7	0	76178
Cortland County	New York	47786	0	14.7	66.3	30	5.87	0	52451
Saratoga County	New York	229869	1	6.6	73.8	23.7	4.02	1	77548
Tioga County	New York	48578	0	11.2	80	13.5	5.18	1	57153
Alexander County	North Carolina	37286	1	14.7	79.9	2.2	3.67	1	44523
Alleghany County	North Carolina	11031	1	21	74	6.2	5.16	0	38944
Divide County	North Dakota	2288	0	13	81	7.3	1.66	0	54223
Sheridan County	North Dakota	1353	1	15.4	86.1	4.4	4.53	0	49750
Stutsman County	North Dakota	21087	0	11.1	68.7	24.3	2.32	0	56088
Athens County	Ohio	66597	1	30.2	58.6	23.6	6.05	0	37191
Medina County	Ohio	178371	1	6.2	81.8	13.4	4.73	1	71595
Caddo County	Oklahoma	29173	0	20.8	71.6	7.1	4.49	0	41626
Jefferson County	Oklahoma	6183	0	20.9	77.9	7.3	5.59	0	35933
Oglala Lakota County	South Dakota	14354	1	12.2	51.3	3.8	4.9	0	42231
Polk County	Tennessee	16757	1	17	80.7	4	4.56	1	42307
Anderson County	Texas	57741	0	15.7	73.7	8	3.62	0	42313
Andrews County	Texas	17722	1	11.9	79.9	9.5	3.06	0	70753
Brown County	Texas	38053	1	16.4	72.5	10.2	3.84	0	43062
Dickens County	Texas	2209	0	16.6	80.4	3.5	4.69	0	43088
Gaines County	Texas	20638	1	11	73	6.3	3.03	0	58167
Hall County	Texas	3071	0	22.2	67	8.8	6.2	0	31324
Hill County	Texas	35852	1	17.5	76.5	5.5	3.88	0	45970
Howard County	Texas	36040	0	13.9	68.9	11.6	4.3	0	50855
Hunt County	Texas	93872	1	18.8	70.5	14.7	3.92	1	49319
Montgomery County	Texas	570934	1	10.3	75.6	13.5	4.33	1	74323
Smith County	Texas	227727	1	16.3	69.4	16.5	4.06	1	50742
Swisher County	Texas	7515	0	22.2	69.3	8.4	4.06	0	37883
Tyler County	Texas	21539	1	15.8	81.7	3.1	7.31	0	44396
Bath County	Virginia	4297	0	9.3	87	0.9	3.3	0	44483
Charlotte County	Virginia	12119	0	22.7	77.9	4.1	4.74	0	38350
Franklin County	Virginia	56445	1	14.8	78.5	7.8	3.97	1	51208
Mecklenburg County	Virginia	30686	0	16.9	75.1	4.4	5.25	0	41126
Wythe County	Virginia	28882	0	15.2	77	7.2	5.21	0	46119
Chesapeake	Virginia	240397	1	9.6	74.9	16.8	3.87	1	72214
Manassas Park	Virginia	16591	1	10.3	71.2	16.6	3.35	1	79131
Poquoson	Virginia	12053	0	4.9	84.8	6.1	3.49	1	88328
Hampshire County	West Virginia	23471	0	16.9	67.6	5.1	3.93	1	36575
Mason County	West Virginia	26801	0	19.3	78.1	6.9	6.7	0	38977
Calumet County	Wisconsin	50067	1	5.9	83.6	13.3	2.77	1	70662
Vernon County	Wisconsin	30759	1	16.6	79	10.3	3.07	0	49996
Waukesha County	Wisconsin	400621	1	5	77.7	22.1	2.9	1	81140
Natrona County	Wyoming	79547	0	9.9	70.4	15.8	5.31	1	59400

Calculate the test statistic (Round answer to 2 decimal places) Calculate the p-value (Round answer to 4 decimal places) This test statistic leads to a decision to

• accept the null
• reject the null
• fail to reject the null

Provide Explanation with : 1. Hypotheses :

2. Assumption check:

3. Decision rule:

4. Descriptive statistics:

5. Decision:

6. Conclusion:

***Sample just like below

Hypotheses:

H0: 0.44

H1: < 0.44

Assumption check:

1) "Success" does come from a binomial distribution.

2) 0=350(.44) = 154 5 3) 0=350(.66) = 196 5 Thus, we can employ the central limit theory that says the distribution of is approximately normal and inferences on the actual proportion of counties which are considered inside a metro area should be valid.

Decision rule:

If the p-value is less than the pre-determined alpha of 0.01, we will reject the null hypothesis.

Descriptive statistics:

= 0.3829

z = -2.15

p-value = 0.0156

Decision:

Because the p-value of 0.0156 is greater than the pre-determined alpha of 0.01, we fail to reject the null hypothesis.

Conclusion :

We can not conclude that the actual proportion of counties that are considered inside a metro area was less than 44%