Question

Problem (2). 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 were 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 pressure for the 12 rats are shown in the accompanying table. Do the data provide sufficient evidence to indicate that rats exposed to a 5°C environment have a higher mean blood pressure than rats exposed to a 26°C environment? Test by using α = .05.

26°C			5°C
Rat	Blood Pressure		Rat	Blood Pressure
1	152		7	384
2	157		8	369
3	179		9	354
4	182		10	375
5	176		11	366
6	149		12	423

Answer 1

Define , : Population mean blood pressure of rats exposed to C environment .

: Population mean blood pressure of rats exposed to C environment .

   :  Sample mean blood pressure of rats exposed to C environment .

   :  Sample mean blood pressure of rats exposed to C environment .

   : Sample standard deviation of rats exposed to C environment .

   : sample standard deviation of rats exposed to   C environment .

To test :

Test statistic :

where , and

Degrees of freedom = 10

We reject the null hypothesis or H₀ if the observed value of , where ,

The value of the test statistic :

Critical value :

Now ,

Hence we reject the null hypothesis or H₀ .

Thus we have sufficient evidence to support the claim that rats exposed to a 5°C environment have a higher mean blood pressure than rats exposed to a 26°C environment .