Question

Question 2. Let a sample of size 7, X1, ...., X7 (i.i.d) be a random variable X which gives the volume in (ml) of blood for a paraplegic man who participates in
vigorous physical activity which is normally distributed with an average µX and
variance σ
2
X. Another sample of size 10, Y1, ...., Y10 (i.i.d) as a random variable
Y which gives the volume of blood (in ml) for a normal man, who is busy in his
ordinary activities and which is normally distributed with an average µY and variance σ
2
Y
.
Using the following data:
x1 = 1612; x2 = 1352; x3 = 1456; x4 = 1222; x5 = 1560; x6 = 1456; x7 = 1924 and
y1 = 1082; y2 = 1300; y3 = 1092; y4 = 1040; y5 = 910; y6 = 1248; y7 = 1092; y8 = 1040; y9 =
1092; y10 = 1288.
(a) Find a point estimator of µX - µY
(b) Find a 95% confidence interval for µX - µY:

Answer 1

(a)

From the given data, the following statistics are calculated:

n1 = 7

1 = 10582/7 = 1511.7143

s1 = 206.3352

n2 = 10

2 =11184/10 = 1118.4

s2 = 117.3364

So,

a point estimator of µX - µY is given by:

So,

Answer is:

393.3143

(b)

Pooled Standard Deviation is given by:

= 0.05

df = 7 + 10 - 2 = 15

From Table, critical values of t = 2.131

Confidence Interval:

= (226.3057, 560.3229)

So,

Answer is:

(226.3057, 560.3229)