Question

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.2 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 180 engines and the mean pressure was 6.3 pounds/square inch. Assume the standard deviation is known to be 0.9. A level of significance of 0.05 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.

Answer 1

Answer:

Given:

mean, u = 6.2

sample size, n = 180

Sample mean, X' = 6.3

s.d $\sigma$ = 0.9

Significance level = 0.05

The null and alternative hypothesis will be:

H0 : u = 6.2

H1 : u > 6.2

Degree of freedom = 180 - 1 = 179

Using t table, the t critical value,

t> t(0.05, 179) = 1.6534

The test statistic:

$t = \frac{X' - u}{\frac{\sigma}{\sqrt{n}}}$

$T = \frac{6.3 - 6.2}{\frac{0.9}{\sqrt{180}}} = 1.4907$

Since the test statistic(t calculated value) 1.4907 < t critical value (1.6534), we fail to reject the null hypothesis H0.