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 6.5 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 26 engines and the mean pressure was 6.6 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answer 1

The calculated value t = 0.510 < 2.7874 at 0.01 level of significance

The null hypothesis is accepted at 0.01 level of significance

The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch

Explanation:

Step:-1

Given that mean of the population (μ) = 6.5 pounds/ square inch

Given that the sample size 'n' = 26

Given that mean of the sample ( x⁻) = 6.6 pounds/ square inch

Given that the standard deviation of the sample (σ) = 1.0

t₀.₀₁ = 2.7874

Step:-2

Null hypothesis:H₀: μ = 6.5

Alternative Hypothesis:H₁: μ ≠6.5

Test statistic

`t = (x^(-)-mean )/((S)/(√(n) ) )`

`t = (6.6-6.5)/((1.0)/(√(26) ) )`

t = 0.510

The calculated value t = 0.510 < 2.7874 at 0.01 level of significance

Final answer:-

The calculated value t = 0.510 < 2.7874 at 0.01 level of significance

The null hypothesis is accepted at 0.01 level of significance

The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch