Question

The mean water temperature downstream from a power plant cooling tower discharge pipe should be no more than 97^oF. Past experience has indicated that the standard deviation of temperature is 2^oF. The water temperature is measured on 4 randomly chosen days, and the average temperature is found to be 94^oF.

Conduct a hypothesis testing using the 7 steps at a 5% significance level.

Answer 1

Solution :

Given that,

Population mean = = 97

Sample mean = = 94

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,

Ho: 97

Ha: 97

The test statistics,

t = ( - )/ (s/)

= ( 94 - 97 ) / ( 2 / 4 )

= -3

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= -2.353

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.