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A hydraulic press is operating correctly when the standard deviation of the pressure is less than 120 pounds-per-square-inch (psi).Suppose you take a random sample of 15 measurements throughout the day of the psi and find the standard deviation to be 148.Suppose you want to test whether the press is operating correctly.
-For a two-tailed test at the 0.05 significance level,what is the rejection region when n is large and the population standard deviation is known?
A)between -1.645 and +1.645
B)between -1.96 and +1.96
C)less than -1.645 or greater than +1.645
D)less than -1.96 and greater than 1.96

Question

Quizplus · Accepted Answer

Since n is large (n=15>10) and population standard deviation is known, we use a z-test.

At a 0.05 significance level for a two-tailed test, we split the rejection region equally between the left and right tails of the distribution.

Using a standard normal distribution table, the critical values for a two-tailed test at the 0.05 level of significance are ±1.96.

Therefore, the rejection region is less than -1.96 and greater than 1.96. Choice D is the correct answer.

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