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 4.4 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 4.5 pounds/square inch. Assume the variance is known to be 0.64. A level of significance of 0.1 will be used. Make a decision to reject or fail to reject the null hypothesis.

Make a decision.

Answer 1

In this question, we will use the t-test to test the null and the alternative hypothesis statement about the population mean at 10% level of significance.

Given that,

• Population mean, μ=4.0
• Sample size, n=180
• mean, =4.5
• variance, s²=0.64

Level of significance, α=0.1

The null hypothesis is,

H₀:μ≤4.0

The alternative hypothesis is,

H₁:μ>4.0

t-test statistic is defined as:

t=( −μ)/(s/√n)

Now,

t=(4.5−4.0)/(0.8/√180)

t=8.385

Excel function for the P-value:

=TDIST(8.385,179,1)

P−value=0 (approximately)

The P-value is less than 10% level of significance. we reject the null hypothesis at 10% level of significance.