# A Template for a Hypothesis Test and a Confidence Interval ```Template for a Confidence Interval:
Variable:_________________________
Parameter:
________________________
Point Estimate:
________________________
Standard Error
________________________
Inference:
Estimation
Formula (Page Number)________________________
Formula
Substitution:
Conclusion: We are ____% confident
CONFIDENCE
that the ______________________
PARAMETER
____________________________
DEPENDENT VARIABLE
falls in the range:________________
RANGE
Example Using Template for a Confidence Interval:
You wish to estimate the average annual return on a population of stocks. From a
random sample of size 50, you find an average of 14.75 and a standard deviation
of 8.18. With 95% confidence what is the average annual return?
Dependent Variable: annual return
Parameter:

Point Estimate
x = 14.75
Standard Error
Sx =
Inference:
Estimation
s
8.18
=
=1.1569
n
50
Formula (Page Number) ________
Formula
( x )  (tn-1,/2) S x
Substitution:
14.75 &plusmn; t49, 0.025 (1.1569)
14.75 &plusmn; 2.009 (1.1569)
14.75 &plusmn; 2.32
12.43 to 17.07
Conclusion: We are 95% confident
that the average
annual return
falls in the range: 12.43 to 17.07 percent.
or
Conclusion: We are 95% confident
that the average
annual return
is 14.75
with a margin of error of &plusmn; 2.32
CONFIDENCE
PARAMETER
VARIABLE
RANGE
CONFIDENCE
PARAMETER
VARIABLE
ESTIMATE VALUE
MARGIN OF ERROR
Template for a Hypothesis Test:
Variable:_________________________
Parameter:
________________________
Point Estimate:
________________________
Standard Error
________________________
Inference:
Hypothesis Test
Ho: _________
Rejection Region: Reject Ho if
Ha: _________
_________________________
Test Statistic: Formula (page)___________
Formula
Substitution:
Conclusion: At = _____
SIGNIFICANCE LEVEL
we can (not) say that
DECISION
that the ______________________
PARAMETER
____________________________ DEPENDENT VARIABLE
____________________________
PARAMETER VALUES IN Ha
Example Using Template for a Hypothesis Test:
In the past the machines you use can process 450 items on average per day. A new
company says that its machine will outperform your current ones. You take a
random sample of size 50 and find a sample mean of 460.38 with a standard
deviation of 38.83. Is there evidence that the new machine is better?
Variable:
number of packages processed
Parameter:

Point Estimate
x = 460.38
Standard Error
Sx =
Inference:
s
38.83
=
= 5.4914
n
50
Hypothesis Test
Ho:  ≤ 450
Rejection Region: Reject Ho if
Ha:  &gt; 450
t* &gt; t(n-1,) = t (49, 0.05, ) = 1.676
Test Statistic: Formula (page) _______
Formula
t* = ( x -  ) / S x
Substitution: t* = (460.38-450) / (1.676)
= 1.89
Conclusion: At = 0.05
we can say that
that the mean
number of packages processed
is greater than 450 packages.
SIGNIFICANCE LEVEL
DECISION
PARAMETER
VARIABLE
PARAMETER VALUES IN Ha
```