Question

You want to compare the efficiency of two combustion engine coolant systems. It is hypothesized that there is no difference in the average temperature of the engines that use both cooling systems, after 2 hours of continuous operation. An experiment was applied and the following results were obtained:

	System A	System B
Sample size	26	17
Average temperature	56,3°C	61,7°C
Sample deviation	12,4°C	8,1°C

a) Determine the regions of acceptance and rejection of the hypothesis, using a significance level of 2%. Suppose the population deviations are equal.

b) Explain whether the evidence supports the hypothesis that there is no difference in the average temperature of the engines that use both cooling systems, after 2 hours of continuous operation. Use a confidence level of 98%, under the assumption that the population deviations are equal.

c) Determine the regions of acceptance and rejection of the hypothesis, using a significance level of 2%. Suppose the population deviations are different.

d) Explain whether the evidence supports the hypothesis that there is no difference in the average temperature of the engines that use both cooling systems, after 2 hours of continuous operation. Use a confidence level of 98%, and assume that the population deviations are different.

a) Determine the regions of acceptance and rejection of the hypothesis, using a significance level of 2%. Suppose the population deviations are equal.

b) Explain whether the evidence supports the hypothesis that there is no difference in the average temperature of the engines that use both cooling systems, after 2 hours of continuous operation. Use a confidence level of 98%, under the assumption that the population deviations are equal.

c) Determine the regions of acceptance and rejection of the hypothesis, using a significance level of 2%. Suppose the population deviations are different.

d) Explain whether the evidence supports the hypothesis that there is no difference in the average temperature of the engines that use both cooling systems, after 2 hours of continuous operation. Use a confidence level of 98%, and assume that the population deviations are different.

Answer 1

(a) Reject Ho if t > 2.42.

(b) The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

A	B
56.3	61.7	mean
12.4	8.1	std. dev.
26	17	n
	41	df
	-5.4000	difference (A - B)
	119.3600	pooled variance
	10.9252	pooled std. dev.
	3.4076	standard error of difference
	0	hypothesized difference
	-1.585	t
	.1207	p-value (two-tailed)

The p-value is 0.1207.

Since the p-value (0.1207) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is no difference in the average temperature of the engines that use both cooling systems, after 2 hours of continuous operation.

(c) Reject Ho if t > 2.42.

(d) The hypothesis being tested is:

H0: µ1 = µ2

H1: µ1 ≠ µ2

A	B
56.3	61.7	mean
12.4	8.1	std. dev.
26	17	n
	40	df
	-5.4000	difference (A - B)
	3.1262	standard error of difference
	0	hypothesized difference
	-1.727	t
	.0918	p-value (two-tailed)

The p-value is 0.0918.

Since the p-value (0.0918) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is no difference in the average temperature of the engines that use both cooling systems, after 2 hours of continuous operation.