Chapter 14, Problem 13CQ

Blood Pressure Divide the individuals into subgroups of six males and six females. Find the means of their blood pressures.

To determine

The sample mean of six males and six females.

To compare: The resultswith the population means.

Answer to Problem 13CQ

The sample mean of male blood pressure is 144.33 and the sample mean of female blood pressure is 144.66.

The sample mean of male blood pressure is greater than the population mean of male blood pressure and also sample mean of female blood pressure is greater than the population mean of female blood pressure.

Explanation of Solution

Given info:

The blood pressure data for 100 individuals are listed.

Calculation:

Answers will vary. One of the possible answers is given below:

Divide the data into two groups according to males and females.

Group1 (Males):

ID	Blood Pressure
2	120
4	129
7	131
8	163
11	148
14	142
15	156
16	135
19	122
21	122
22	119
25	118
26	118
27	120
31	131
32	151
33	148
36	129
37	138
39	156
43	141
46	136
48	116
49	132
50	135
53	117
54	121
55	130
58	136
59	119
60	123
63	115
65	158
68	142
70	128
71	125
75	131
76	118
77	116
79	123
80	127
84	129
85	121
86	115
89	120
90	123
93	127
94	142
97	163
100	129

Group2 (females):

ID	Blood pressure
1	126
3	128
5	119
6	136
9	132
10	138
12	115
13	149
17	156
18	153
20	142
23	135
24	133
28	118
29	120
30	132
34	142
35	131
38	130
40	126
41	114
42	116
44	110
45	113
47	152
51	141
52	121
56	118
57	115
61	117
62	121
64	141
66	117
67	120
69	123
72	128
73	135
74	143
78	120
81	116
82	123
83	131
87	133
88	138
91	133
92	120
95	111
96	142
98	151
99	147

Select any six males from group 1 and six females from group 2 at random.

Male subgroup1:

ID Number	Gender	Blood pressure
8	M	163
11	M	148
14	M	142
15	M	156
16	M	135
19	M	122

Female subgroup2:

ID Number	F	Blood pressure
13	F	149
17	F	156
18	F	153
20	F	142
23	F	135
24	F	133

The sample mean of male blood pressure is,

$\begin{array}{c}\text{Sample}\text{mean}\text{of}\text{male}\text{blood}\text{pressure}=\frac{\text{Sum}\text{of}\text{the}\text{samples}\text{of}\text{male}\text{blood}\text{pressure}}{\text{Number}\text{of}\text{samples}}\\ \text{=}\frac{\text{866}}{\text{6}}\\ \text{=144}\text{.33}\end{array}$

The population mean of male blood pressure is,

$\begin{array}{c}\text{Population}\text{mean}\text{of}\text{male}\text{blood}\text{pressure}=\frac{\text{Sum}\text{of}\text{all}\text{male}\text{blood}\text{pressure}\text{values}}{\text{Number}\text{of}\text{Values}}\\ \text{=}\frac{\text{6,554}}{\text{50}}\\ \text{=131}\text{.08}\end{array}$

The sample mean of female blood pressure is,

$\begin{array}{c}\text{sample}\text{mean}\text{of}\text{female}\text{blood}\text{pressure}=\frac{\text{Sum}\text{of}\text{the}\text{samples}\text{of}\text{female}\text{blood}\text{pressure}}{\text{Number}\text{of}\text{samples}}\\ \text{=}\frac{\text{868}}{\text{6}}\\ \text{=144}\text{.6667}\end{array}$

The population mean of male blood pressure is

$\begin{array}{c}\text{Population}\text{mean}\text{of}\text{female}\text{blood}\text{pressure}=\frac{\text{Sum}\text{of}\text{all}\text{female}\text{blood}\text{pressure}\text{values}}{\text{Number}\text{of}\text{Values}}\\ \text{=}\frac{\text{6,471}}{\text{50}}\\ \text{=129}\text{.42}\end{array}$

Comparison of means:

The sample mean of male blood pressure is 144.33 and the population mean of male blood pressure is131.08, the sample mean of female blood pressure is 144.66 and the population mean of female blood pressure is 129.42.

By comparing of means it is clear that there is a larger difference between the sample mean and the population mean of blood pressure of males. Also there is a larger difference between the sample mean and the population mean of blood pressure of females.