Compare the statistical likelihood of a man or a woman

Question

Assignment:

T-tests

On the last table are data on cancer rates by region for the whole of Scotland. The data were collected in 2000 and are expressed as rates per 100,000. If you were to compare the statistical likelihood of a man or a woman contracting lung cancer using a t-test Excel would produce the following output.

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	86.99158	50.35315
Variance	461.3188	146.3005
Observations	29	29
Hypothesized Mean Difference	0
df	44
t Stat	8.004239
P(T<=t) one-tail	1.99E-10
t Critical one-tail	1.68023
P(T<=t) two-tail	3.98E-10
t Critical two-tail	2.015367

This analysis would tell you the following:

The average rate of lung cancer per 100,000 men in Scotland =        87

The average rate of lung cancer per 100,000 women in Scotland =   50

Because the t-statistic associated with the above is 8.00 and the critical point at the 0.05% level for statistical significance (with 2 tails) is 2.02 then there is a statistically significant difference in lung cancer rates between men and women in Scotland. Indeed the probability value (P(T<=t) two-tail) associated with the above analysis is 0.0000000000398 or 3.98 * 10^-10 . This is much less than 0.05 and is also less than 0.01 (the two limits commonly used by scientists).

The above output could therefore be summarised in a table as follows:

Statistical Comparison of Lung Cancer Rates between Men and Women in Scotland
Mean rate (per 100,000) for Men =	87
Mean rate (per 100,000) for Women =	50
t-value at 5% level =	2.02
t-statistic generated from t-test =	8.00
p-value associated with t-test =	p < 0.01
Conclusion =	There is a significant difference in lung cancer rates between men and women in Scotland.

Complete the following tables based on the data for other cancers.

Statistical Comparison of Stomach Cancer Rates between Men and Women in Scotland
Mean rate (per 100,000) for Men =
Mean rate (per 100,000) for Women =
t-value at 5% level =
t-statistic generated from t-test =
p-value associated with t-test =
Conclusion =

Statistical Comparison of Large Bowel Cancer Rates between Men and Women in Scotland
Mean rate (per 100,000) for Men =
Mean rate (per 100,000) for Women =
t-value at 5% level =
t-statistic generated from t-test =
p-value associated with t-test =
Conclusion =

Statistical Comparison of Bladder Cancer Rates between Men and Women in Scotland
Mean rate (per 100,000) for Men =
Mean rate (per 100,000) for Women =
t-value at 5% level =
t-statistic generated from t-test =
p-value associated with t-test =
Conclusion =

Statistical Comparison between the rate of Stomach Cancer and the rate of Cervical Cancer in the Female population in Scotland
Mean rate of Stomach Cancer =
Mean rate of Cervical Cancer =
t-value at 5% level =
t-statistic generated from t-test =
p-value associated with t-test =
Conclusion =

Statistical Comparison between the rate of Large Bowel Cancer and the rate of Prostate Cancer in the Male population in Scotland
Mean rate of Large Bowel Cancer =
Mean rate of Prostate Cancer =
t-value at 5% level =
t-statistic generated from t-test =
p-value associated with t-test =
Conclusion =

Cancer Registrations by local council area: year ending 31 December 2000
Rates per 100 000		Men						Women
Local council area		Lung	Stomach	Large bowel	Bladder	Prostate		Lung	Stomach	Large bowel	Bladder	Breast	Ovary	Cervix uteri
All Areas		88.9	20.7	66.2	18.0	68.3		52.6	9.0	42.0	5.7	117.5	19.2	10.2
Aberdeen City		84.4	22.7	71.2	15.1	70.9		58.5	11.7	46.7	5.7	112.8	13.0	7.6
Aberdeenshire		61.6	22.5	62.4	24.0	79.1		36.8	5.7	50.3	2.1	144.7	18.0	9.2
Angus		66.8	17.3	83.6	17.0	67.8		36.7	8.7	48.4	0.0	95.1	29.7	0.0
Argyll & Bute		102.9	20.6	59.9	14.7	91.9		53.3	0.0	55.8	0.0	139.2	10.4	11.9
Scottish Borders		65.8	18.0	62.6	17.5	68.7		51.4	5.1	49.4	7.1	87.3	22.9	15.9
Clackmannanshire		132.2	0.0	55.4	27.3	101.5		54.3	12.5	32.5	0.0	81.7	23.1	0.0
Dumfries & Galloway		66.2	17.5	59.8	18.5	47.9		30.9	0.0	34.0	4.3	128.4	17.6	11.1
Dundee City		70.9	26.6	73.7	18.5	58.9		43.6	13.1	37.5	7.9	105.2	14.7	18.0
East Ayrshire		93.9	30.1	50.9	14.4	69.2		44.4	7.0	41.6	7.8	126.8	14.8	6.9
East Dunbartonshire		78.0	23.3	51.7	12.8	66.2		60.4	0.0	41.9	6.2	154.5	17.4	9.6
East Lothian		88.5	25.9	68.4	21.7	94.6		47.2	14.0	52.4	9.6	183.8	28.5	13.8
East Renfrewshire		70.9	23.9	60.9	19.5	61.3		38.6	0.0	26.9	0.0	174.6	19.5	0.0
Edinburgh City		88.3	15.0	61.3	16.4	92.0		55.3	5.7	42.6	3.7	112.9	19.4	10.2
Falkirk		86.8	20.0	73.3	14.5	76.9		47.0	10.3	29.8	7.6	103.5	20.4	6.5
Fife		75.1	21.9	78.0	20.9	54.6		43.5	8.3	46.3	4.6	154.5	22.6	7.1
Glasgow City		132.6	26.4	70.7	19.3	57.3		86.8	12.1	39.6	5.5	116.2	20.8	11.2
Highland		63.3	15.4	77.1	17.0	101.6		35.0	13.3	42.2	10.7	119.8	20.1	10.1
Inverclyde		116.0	34.0	65.2	15.0	47.7		48.1	10.1	31.7	10.3	92.6	11.6	0.0
Midlothian		105.8	0.0	54.9	16.8	61.1		69.1	8.8	46.7	10.1	87.8	11.7	0.0
Moray		76.4	15.4	67.8	20.5	57.0		53.6	0.0	51.8	0.0	97.3	24.5	0.0
North Ayrshire		78.4	22.6	62.5	17.5	52.3		48.9	8.0	43.3	8.1	108.4	14.9	10.7
North Lanarkshire		119.2	21.9	60.6	16.2	48.5		59.8	12.4	35.2	8.8	123.3	15.0	12.5
Perth and Kinross		71.8	24.3	87.4	15.5	63.6		37.2	10.1	48.1	7.2	126.2	22.2	0.0
Renfrewshire		89.3	26.3	59.7	14.6	63.0		60.5	10.9	44.6	4.8	115.6	19.8	10.7
South Ayrshire		74.1	9.8	63.6	16.2	65.9		39.4	6.4	40.6	0.0	66.4	26.1	15.7
South Lanarkshire		95.7	17.1	61.5	18.0	70.3		52.0	8.5	37.1	5.9	103.2	16.8	10.5
Stirling		49.9	21.4	44.8	22.3	94.9		41.3	8.1	37.1	9.1	62.7	17.2	14.0
West Dunbartonshire		106.6	20.5	57.4	15.6	44.0		64.2	13.6	50.1	0.0	148.1	21.1	13.5
West Lothian		111.2	11.4	76.2	23.9	83.9		62.4	11.2	37.6	5.4	69.5	24.9	16.4