Answer:
There is not sufficient evidence at the 0.05 significance level that the valve does not perform to the specifications.
Step-by-step explanation:
Null hypothesis: The valve perform to the specifications.
Alternate hypothesis: The valve does not perform to the specifications.
The population standard deviation is known, hence a z-test is used.
Test statistic (z) = (sample mean - population mean) ÷ (population sd/√n)
sample mean = 5.4
population mean = 5.5
population sd = 0.8
n = 200
z = (5.4 - 5.5) ÷ (0.8/√200) = -0.1 ÷ 0.0566 = -1.77
The test is a two-tailed test. From the standard normal distribution table, the critical values at 0.05 significance level are -1.96 and 1.96.
Decision rules:
Reject the null hypothesis if the test statistic falls outside the region bounded by the critical values.
Fail to reject the null hypothesis if the test statistic falls within the region bounded by the critical values.
Conclusion:
Fail to reject the null hypothesis because the test statistic -1.77 falls within the region bounded by the critical values -1.96 and 1.96.
There is not sufficient evidence at the 0.05 significance level that the valve does not perform to the specifications.
