In: Statistics and Probability
The mean water temperature downstream from a power plant cooling tower discharge pipe should be no more than 97oF. Past experience has indicated that the standard deviation of temperature is 2oF. The water temperature is measured on 4 randomly chosen days, and the average temperature is found to be 94oF.
Conduct a hypothesis testing using the 7 steps at a 5% significance level.
Solution :
Given that,
Sample standard deviation = s = 2
Sample size = n = 4
Level of significance =
= 0.05
This is a left tailed test.
The null and alternative hypothesis is,
The test statistics,
= -3
Critical value of the significance level is α = 0.05, and the critical value for a two-tailed test is
Since it is observe that, t = -3 <
= -2.353, It is then concluded that the null hypothesis is
rejected.
p-value = 0.0288
The p-value = 0.0288 <
= 0.05 It is concluded that the null hypothesis is rejected.
Conclusion:
It is concluded that the null hypothesis Ho is rejected, Therefore, there is enough evidence to claim that the population
mean μ is less than 97, at the 0.05 significance level.