Question

Annual Income			SAT Scores
Men	Women		Men	Women
$83,173	$78,980		600	960
$87,335	$73,791		1050	530
$75,573	$62,553		820	710
$88,051	$75,179		730	680
$75,884	$58,778		530	790
$61,595	$110,787		680	1140
$68,993	$64,852		860	940
$83,185	$79,700		1050	420
$87,259	$55,352		910	820
$87,418	$63,386		590	880
$108,114	$78,803		960	890
$97,643	$92,505		1040	1300
$71,920	$94,666		840	1030
$71,516	$69,928		940	740
$79,982	$75,812		760	770
$84,823	$108,581		430	800
$80,256	$100,172		900	600
$69,839	$79,343		1090	1280
$71,071	$72,949		850	850
$79,194	$76,487		780	1000
$58,381	$112,624		710	710
$78,821	$60,996		820	710
$111,731	$47,339		890	920
$79,248	$53,329		840	820
$84,120	$82,489		920	880
$94,918	$82,676		590	1040
$89,201	$96,579		500	800
$82,576	$61,109		980	950
$77,183	$88,520		740	680
$71,012	$88,843		640	1170
$70,972	$69,788		780	610
$90,310	$43,336		700	950
$109,794	$125,325		980	950
$82,200	$79,454		950	980
$71,855	$69,205		810	790
$95,012	$81,778		810	960
$63,326	$80,999		860	1050
$74,356	$91,826		900	790
$68,689	$97,986		800	660
$84,632	$63,485		800	850
$93,572	$71,393		1080	510
$84,828	$80,986		920	1120
$87,006	$101,375		610	930
$94,446	$76,110		670	780
$68,206	$92,437		850	1330
$111,346	$103,105		880	1070
$89,986	$73,283		590	1000
$59,885	$84,225		710	750
$74,106	$75,993		850	670
$101,167	$100,103		840	1000
$87,155	$75,598		850	650
$80,721	$98,321		1000	820
$71,357	$56,366		1140	940
$62,350	$63,702		640	630
$74,943	$64,041		840	930
$92,021	$78,423		680	850
$96,529	$61,274		880	970
$64,590	$73,354		970	550
$83,394	$77,211		1000	410
$92,443	$73,844		740	830
$84,097	$82,373		810	690
$95,639	$83,032		760	650
$99,955	$72,780		960	700
$82,655	$70,057		970	1060
$71,107	$85,709		750	1110
$86,014	$51,100		920	640
$61,463	$70,567		1110	640
$86,042	$69,850		610	1400
$77,772	$62,246		810	860
$82,764	$83,369		920	670
$81,081	$86,006		810	760
$87,314	$74,516		830	900
$119,195	$101,714		1030	790
$86,846	$72,088		830	1140
$90,834	$90,146		920	760
$95,561	$118,558		770	810
$84,543	$76,717		1060	790
$56,569	$48,808		850	1170
$97,319	$25,681		590	780
$85,499	$74,953		880	760
$88,545	$82,735		850	830
$76,991	$75,645		720	1020
$83,179	$74,220		890	820
$73,829	$77,590		730	970
$92,728	$59,025		880	520
$58,302	$71,728		760	920
$74,035	$76,149		920	880
$85,540	$92,157		740	400
$98,551	$90,949		850	640
$66,331			920
$95,954			940
$72,660			750
$95,005			950
$88,832			780
$88,460			1200
$82,142			810
$88,822			710
$52,018			890
$83,809			1020
$67,248			660
$93,338			470
$95,657			880
$86,171			1110

Using the male-female wages and SAT scores shown above, complete the following:

1. Calculate the 5-number summary for each of the 4 columns of data, construct a box plot for each of them as well.

2. Using the box plots, can you draw any conclusions about the relative pay of men and women?

3. Is there a correlation between annual income and SAT scores for each sex? Does the value of the correlation tell you anything about the relationship between annual income and SAT scores?

Answer 1

Result:

Using the male-female wages and SAT scores shown above, complete the following:

1. Calculate the 5-number summary for each of the 4 columns of data, construct a box plot for each of them as well.

Descriptive statistics
	Men INCOME	Women Income	Men SAT	Women SAT
n	103	89	103	89
mean	82,734.25	77,886.54	832.91	845.17
sample standard deviation	12,766.30	16,778.17	150.77	202.56
minimum	52018	25681	430	400
maximum	119195	125325	1200	1400
1st quartile	73,932.00	69,850.00	740.00	710.00
median	83,809.00	76,149.00	840.00	820.00
3rd quartile	90,148.00	86,006.00	920.00	960.00
interquartile range	16,216.00	16,156.00	180.00	250.00
range	67177	99644	770	1000

2. Using the box plots, can you draw any conclusions about the relative pay of men and women?

From the box plot we infer that relative pay of men are more than women. ( median of men are larger than median of women)

3. Is there a correlation between annual income and SAT scores for each sex? Does the value of the correlation tell you anything about the relationship between annual income and SAT scores?

Correlation Matrix
		Men INCOME	Women Income	Men SAT	Women SAT
	Men INCOME	1.000
	Women Income	.096	1.000
	Men SAT	.073	-.042	1.000
	Women SAT	-.037	.061	-.138	1.000
		89	sample size
		± .208	critical value .05 (two-tail)
		± .272	critical value .01 (two-tail)

correlation between annual income and SAT scores for male is 0.073.

correlation between annual income and SAT scores for female is 0.061.

There is positive correlation for both.

But the very low correlation value shows that there is no association between annual income and SAT scores for both sex.