SOLUTION: An average computer mouse inspector can inspect 45 mice per hour with a population standard deviation of 14 mice per hour. The 44 computer mice inspectors at a particular factory c

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Question 1088019: An average computer mouse inspector can inspect 45 mice per hour with a population standard deviation of 14 mice per hour. The 44 computer mice inspectors at a particular factory can only inspect 38 mice per hour. Does the company have reason to believe that these inspectors are slower than average at α = 0.10?

Yes, because the test value –3.32 falls in the noncritical region.

No, because the test value –1.91 falls in the critical region.

Yes, because the test value –3.32 falls in the critical region.

No, because the test value –1.91 falls in the noncritical region.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Given Info

alpha = 0.10
mu = 45
sigma = 14
n = 44
xbar = 38

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Null Hypothesis
H0: mu >= 45

Alternative Hypothesis
H1: mu < 45 (claim is made here)

This is a left tailed Z test for the mean (mu)
We will reject the null (H0) if the test statistic is in the critical region Z < -1.28
Use a calculator or table to find the critical value -1.28

If you use a table like this one, then look at the column that has "one tail = 0.10" and look at the second to bottom value in this column to see 1.282. I'm going to round that to 1.28 and change it to a negative value to get -1.28. This is so I can ensure I have the left portion.

This means P(Z < -1.28) = 0.10 approximately

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Compute the Standard Error

SE = sigma/sqrt(n)
SE = 14/sqrt(44)
SE = 2.11057941204434
SE = 2.110579

That allows us to say

Z = (xbar-mu)/(SE)
Z = (38-45)/(2.110579)
Z = -3.31662543785379
Z = -3.32 Z test statistic (aka Z test value)

The value Z = -3.32 is in the critical region. This is because Z < -1.28 is true when Z = -3.32

Visual confirmation is shown below



So we reject H0.

We have enough sufficient evidence to conclude that the population mean mu is less than 45. So we have enough evidence to conclude that inspectors are slower than average.

Answer is choice C) Yes; test value -3.32 falls in the critical (rejection) region