Question

The income of males in each state of the United States, including the District of Columbia and Puerto Rico, are given in Table 1, and the income of females is given in Table 2 ("Median income of," 2013):

Table 1: Data of Income for Males

$42,951	$52,379	$42,544	$37,488	$49,281	$50,987	$60,705
$50,411	$66,760	$40,951	$43,902	$45,494	$41,528	$50,746
$45,183	$43,624	$43,993	$41,612	$46,313	$43,944	$56,708
$60,264	$50,053	$50,580	$40,202	$43,146	$41,635	$42,182
$41,803	$53,033	$60,568	$41,037	$50,388	$41,950	$44,660
$46,176	$41,420	$45,976	$47,956	$22,529	$48,842	$41,464
$40,285	$41,309	$43,160	$47,573	$44,057	$52,805	$53,046
$42,125	$46,214	$51,630

Table 2: Data of Income for Females

$31,862	$40,550	$36,048	$30,752	$41,817	$40,236	$47,476	$40,500
$60,332	$33,823	$35,438	$37,242	$31,238	$39,150	$34,023	$33,745
$33,269	$32,684	$31,844	$34,599	$48,748	$46,185	$36,931	$40,416
$29,548	$33,865	$31,067	$33,424	$35,484	$41,021	$47,155	$32,316
$42,113	$33,459	$32,462	$35,746	$31,274	$36,027	$37,089	$22,117
$41,412	$31,330	$31,329	$33,184	$35,301	$32,843	$38,177	$40,969
$40,993	$29,688	$35,890	$34,381

Is there enough evidence to show that the mean income of males is more than of females? Test at the 1% level.

(i) Let ?₁= mean income of a male in 2013. Let ?₂ = mean income of a female in 2013. Which of the following statements correctly defines the null hypothesis H_O?

A.  ?₁ ? ?₂ = 0 (?₁ = ?₂)

B.  ?₁ – ?₂< 0 (?₁ < ?₂)

C.  ?₁ ? ?₂ > 0 (?₁ > ?₂)

D.  ?₁ + ?₂= 0

Enter letter corresponding to correct answer

Answer ____________

(ii)   Let ?₁= mean income of a male in 2013. Let ?₂ = mean income of a female in 2013. Which of the following statements correctly defines the alternate hypothesis H_A?

A.  ?₁ ? ?₂ = 0 (?₁ = ?₂)

B.  ?₁ – ?₂< 0 (?₁ < ?₂)

C.  ?₁ ? ?₂ > 0 (?₁ > ?₂)

D.  ?₁ + ?₂= 0

Answer ____________

Enter letter corresponding to correct answer

Answer ____________

(iii) Enter the level of significance ? used for this test:

Enter in decimal form.  

Answer ____________

(iv)  For sample from population with mean = ?1 :          Determine sample mean x¯1 and sample standard deviation s1

Enter sample mean in decimal form to nearest hundredth, then comma, then sample standard deviation in decimal form to nearest hundredth.  

Answer ____________

(v)  For sample from population with mean = ?2 :       Determine sample mean x¯2 and sample standard deviation s2

Enter sample mean in decimal form to nearest hundredth, then comma, then sample standard deviation in decimal form to nearest hundredth.  

Answer ____________

(vi) Determine degrees of freedom df :

Enter value in decimal form rounded down to nearest whole number.  

Answer ____________

(vii) Determine test statistic:

Enter value in decimal form rounded to nearest thousandth.

Answer ____________

(viii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest ten-thousandth.  

Answer ____________

(ix) Comparing p-value and ? value, which is the correct decision to make for this hypothesis test?

A. Reject H_o

B. Fail to reject H_o

C. Accept H_o

D. Accept H_A

Enter letter corresponding to correct answer.

Answer ____________

  (x) Select the statement that most correctly interprets the result of this test:

A. The result is not statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the mean income of males is more than of females. .

B. The result is not statistically significant at .01 level of significance. There is not enough evidence to support the claim that the mean income of males is more than of females.

C. The result is statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the mean income of males is more than of females.

D. The result is statistically significant at .01 level of significance. There is not enough evidence to support the claim that the mean income of males is more than of females.

Enter letter corresponding to most correct answer

Answer ____________

Answer 1

(i)

The null hypothesis is

(ii)

The alternative hypothesis is

(iii)

The level of significance is 0.01.

(iv-v)

For sample 1:

	X1	(X1-mean)^2
	42,951	12266175.34
	50,411	15663310.14
	45,183	1613687.496
	60,264	190735158.3
	41,803	21625383.1
	46,176	76900.8361
	40,285	38048048.26
	42,125	18734267.46
	52,379	35113801.98
	66,760	412361658.8
	43,624	8004995.076
	50,053	12957768.1
	53,033	43292320.5
	41,420	25334209.56
	41,309	26463925.38
	46,214	57269.2761
	42,544	15282704.68
	40,951	30275415.34
	43,993	6053125.296
	50,580	17029570.36
	60,568	199224473.8
	45,976	227824.8361
	43,160	10845890.76
	51,630	26798119.36
	37,488	80376783.4
	43,902	6509182.716
	41,612	23438282.52
	40,202	39078876.72
	41,037	29336414.02
	47,956	2258077.236
	47,573	1253705.696
	49,281	7995830.736
	45,494	920275.6761
	46,313	19686.8961
	43,146	10938299.44
	50,388	15481785.4
	22,529	572372609
	44,057	5742301.616
	50,987	20554345.02
	41,528	24258678.6
	43,944	6296636.676
	41,635	23216111.26
	41,950	20279800.96
	48,842	5705839.916
	52,805	40343965.86
	60,705	203110667.9
	50,746	18427187.44
	56,708	105158667
	42,182	18244089.12
	44,660	3215960.756
	41,464	24893214.28
	53,046	43463561.44
Total	2415572	2520976841

For sample 2:

	X2	(X2-mean)^2
	31,862	21613201
	60,332	567440041
	33,269	10510564
	29,548	48483369
	42,113	31382404
	41,412	24019801
	40,993	20088324
	40,550	16313521
	33,823	7225344
	32,684	14645929
	33,865	7001316
	33,459	9314704
	31,330	26842761
	29,688	46553329
	36,048	214369
	35,438	1151329
	31,844	21780889
	31,067	29637136
	32,462	16394401
	31,329	26853124
	35,890	385641
	30,752	33166081
	37,242	534361
	34,599	3655744
	33,424	9529569
	35,746	585225
	33,184	11068929
	34,381	4536900
	41,817	28153636
	31,238	27804529
	48,748	149744169
	35,484	1054729
	31,274	27426169
	35,301	1464100
	40,236	13875625
	39,150	6964321
	46,185	93586276
	41,021	20340100
	36,027	234256
	32,843	13454224
	47,476	120231225
	34,023	6190144
	36,931	176400
	47,155	113294736
	37,089	334084
	38,177	2775556
	40,500	15912121
	33,745	7650756
	40,416	15249025
	32,316	17598025
	22,117	207187236
	40,969	19873764
Total	1898572	1921503512

(vi)

(vii)

Pooled standard deviation is :

and t-statistics will be

(viii)

p-value = 0.0000

(ix)

A. Reject H_o

Since p-value is less than 0.01 so we reject the null hypothesis.

(x)

C. The result is statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the mean income of males is more than of females.