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 6.66.6 pounds/square inch. The valve was tested on 120120 engines and the mean pressure was 6.86.8 pounds/square inch. Assume the variance is known to be 1.001.00. Is there evidence at the 0.050.05 level that the valve performs above the specifications?

Step 2 of 5:

Enter the value of the z test statistic. Round your answer to two decimal places.

Step 3 of 5:

Specify if the test is one-tailed or two-tailed.

Step 4 of 5:

Enter the decision rule.

Step 5 of 5:

Enter the conclusion.

-(Reject Null Hypothesis)

-(Fail to Reject Null Hypothesis)

Answer 1

Null Hypothesis, 6.6

H0 : μ

Alternative Hypothesis, 6.6

Ha : μ>

Here, sample mean, 6.8, Population std. dev., 1, Sample size, n = 120

Test statistic,

z = (6.8 – 6.6)/(1/sqrt(120))

z = 2.19

One tailed test

Here the significance level, 0.05. This is right tailed test; hence rejection region lies to the right.
Z(a) -
1.645 i.e. P(z > 1.645) = 0.05

Reject H0 if test statistic, z > 1.64

P-value = P(z > 2.19)

P-value = 0.0143

Reject H0