Question 1155043
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mu = 260 is the population mean
xbar = 227 is the sample mean
sigma = 40 is the population standard deviation
n = 30 is the sample size


Compute the z score
z = (xbar - mu)/(sigma/sqrt(n))
z = (227-260)/(40/sqrt(30))
z = -4.51871109941762
z = -4.52
The test statistic, or test value, is approximately -4.52


The critical value can be found through <a href="http://www.ttable.org/">this table</a> (tables such as this can be found in the back of your textbook). According to that table, the solution to P(Z < k) = 0.95 is roughly k = 1.645
In other words, P(Z < 1.645) = 0.95
We make this value negative because we are below the mean.
Therefore, the critical value is approximately -1.645
meaning that, P(Z < -1.645) = 0.05



Answer: <font color=red size=4>A) Yes, because the test value -4.52 falls in the critical region.</font> (the boundary is set at the critical value -1.645)


Diagram
<img width="50%" src = "https://i.imgur.com/TlRWXNL.png">
The critical region is another name for the rejection region. 
The null hypothesis is mu = 260, the alternative is mu < 260.
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