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 5.0 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 5.1 pounds/square inch. Assume the standard deviation is known to be 0.6. A level of significance of 0.1 will be used. Determine the decision rule. Enter the decision rule.

Answer 1

A mean pressure of 5.0 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 5.1 pounds/square inch.

Assume the standard deviation is known to be 0.6. A level of significance of 0.1 will be used. Determine the decision rule

. Enter the decision rule.

The standard deviation of the population is unknown, hence a t-test will be used.

Let's calculate the value of test statistic which is:

t = (x - μ0)/(s/√n)
x = sample mean = 5.1
s = 0.6
n = 180
μ0 = Hypothesised value = 5.0

t = (5.1 - 5.0)/(0.6/√180)
t = 2.236

The t-critical value at df = 179 and significance level 0.1 is 2.58

The value of the test statistic is 2.23. The t-critical value is different which is 2.58.

As t-calculated < 2.58, we do not reject the null hypothesis