Question 141513
1. The following information is available.
H0: µ = 50
H1: µ ≠ 50
The sample mean is 49, and the sample size is 36. The population standard deviation is 5. Use a 0.05 significance level.
Answer the questions: 
(a)	Is this a one- or two-tailed test? 
<pre><font color = "indigo"><b>
This is a TWO-tailed test because of the "&#8800;"
(It is one-tailed when H1 has > or <
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(b)	What is the decision rule? 
<pre><font color = "indigo"><b>
We reject H0 if the test statistic is either greater 
than 1.96 or less than -1.96, for those are the z-values
each of which has half the .05, or .025, of area beyond 
them. If the test statistic is between -1.96 and 1.96,
we fail to reject H0.
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(c)	What is the value of the test statistic? 
<pre><font color = "indigo"><b>
{{{z = (xbar-mu)/(sigma/sqrt(n)) = (49-50)/(5/sqrt(36)) = (-1)/(5/6) = (-1)(6/5) = -6/5 = -1.2}}}
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(d)	What is your conclusion (in plain English) regarding H0?
<pre><font color = "indigo"><b>
We fail to reject H0 because -1.2 is between -1.96 and 1.96.

Edwin</pre></font></b>