Question

In an effort to link cold environments with hypertension in humans, a preliminary experiment was conducted to investigate the effect of cold on hypertension in rats. Two random samples of 6 rats each were exposed to different environments. One sample of rats was held in a normal environment at 26°C. The other sample was held in a cold 5°C environment. Blood pressures and heart rates were measured for rats for both groups. The blood pressures for the 12 rats are shown in the accompanying table.

26°C			5°C
Rat	Blood Pressure		Rat	Blood Pressure
1	171		7	364
2	171		8	423
3	172		9	393
4	145		10	393
5	164		11	420
6	176		12	401

(a) Do the data provide sufficient evidence that rats exposed to a 5°C environment have a higher mean blood pressure than rats exposed to a 26°C environment? Use α= .05. (The difference in means is represented by μ₂₆ − μ₅.)

t	=
Rejection region      t	≤
p-value	=

Fail to reject H₀ and conclude there is significant evidence that μ₂₆ is less than μ₅.

Reject H₀ and conclude there is significant evidence that μ₂₆ is less than μ₅.

Fail to reject H₀ and conclude there is no significant evidence that μ₂₆ is less than μ₅.

Reject H₀ and conclude there is no significant evidence that μ₂₆ is less than μ₅.

(b) Evaluate the three conditions required for the test used in part (a).

This answer has not been graded yet.

(c) Provide a 95% confidence interval on the difference in the two population means, μ₂₆ − μ₅.
(  ,  )

Answer 1

a)

H0 : mu1 -mu2=0
Ha: mu1 -mu2 > 0

test statistics:

t = (x1 -x2)/sqrt(s1^2/n2+s2^2/n2)
= (166.5 - 399)/sqrt(11.2205^2/6+ 21.5314^2/6)
= -23.4561

t < -2.015

p value = .00001.

Reject H0 and conclude there is no significant evidence that μ26 is less than μ5.

b)
The data were collected in a random way, each observation must be independent of the others
The sampling distribution must be normal or approximately normal
The population standard deviation must be known.

c)

t value at 95% = 2.5706

CI = (x1 -x2) +/- t * sqrt(s1^2/n2+s2^2/n2)
= (166.5 - 399) +/- 2.5706 * sqrt(11.2205^2/6+ 21.5314^2/6)

= ( -257.9801,-207.0199)