The income of males in each state of the United States, including the District o
ID: 3371871 • Letter: T
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 HO?
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 HA?
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 Ho
B. Fail to reject Ho
C. Accept Ho
D. Accept HA
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 ____________
$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
Explanation / Answer
(i) Since we want to test that the mean income of males is more than of females, so
A. ?1 ? ?2 = 0 (?1 = ?2)
(ii) Let ?1= mean income of a male in 2013. Let ?2 = mean income of a female in 2013. Then
C. ?1 ? ?2 > 0 (?1 > ?2)
(iii) Enter the level of significance ? used for this test: 1%
(iv) For sample from population with mean = ?1 : Determine sample mean x¯1 and sample standard deviation s1
Variable Mean StDev
Males 46453.310 7030.713
(v) For sample from population with mean = ?2 : Determine sample mean x¯2 and sample standard deviation s2
Variable Mean StDev
Females 36511 6138.122
(vi) Determine degrees of freedom df :105-2=102
(vii) Determine test statistic: 7.608
viii) p-value=P(t>7.608|t~t102) =0.000
(ix) p-value=0.000<0.01
A. Reject Ho
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.
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