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Finding the Confidence Interval

Page 1
www.rit.edu/ASC
Page 1 of 2 Instructions on the left pertain to means Instructions on the right pertain to proportions 1. POPULATION a. Identify the parameter of interest: µ : Mean Numerical (Measurement) �� : proportion Categorical (success-failure) b. Describe the variable in context of the problem: µ = mean of the amount of drying time of a particular paint. �� = proportion of people in the community who prefer smoking. c. Define the NULL and ALTERNATIVE Hypotheses:
The Null hypothesis is usually in the form of:
=
��:0
H
hypothesized value
=
��:0
H
hypothesized value NOTE: The alternative hypothesis ( )a
H :
• is the research hypothesis • is what the problem is asking you to show • uses the ��, <, or > inequalities
2. STATISTICAL METHOD a. Determine the level of significance( )�� :
NOTE: If it is not given in the problem, set it to the default value of 0.05.
b. Determine the appropriate test statistic:
Population mean Population Proportion
When �� known:
( )
( )
x hypothesized value z n
��
- =
( ) ( )( )
. 1 . p hypothesized value z hyp value hyp value n
- = -
When �� unknown:
( )
( )
x hypothesized value t s n
- =
How to Perform a Statistical Hypothesis Test

Page 2
www.rit.edu/ASC
Page 2 of 2 3. SAMPLE a. Calculate or identify the descriptive statistics: Descriptive statistics needed:
• the sample mean • standard deviation • sample size
Descriptive statistics needed:
• the sample proportion • sample size
b. Check the conditions for normality: population is normal OR n �� 30 n(hyp value) �� 10 AND n(1-hyp value) ��10 4. STATISTICAL RESULTS a. Compute the test statistic using the formula from step 2.
b. Determine the p-value based on the computed value of the test statistic: NOTE: Calculator shortcuts for test statistic and p-value:
5. CONCLUSION a. Make a decision:
Check to see if the p-value is less than or equal to the level of significance, ��. In other words, is the p-value �� ��? If it is, reject H0. If it is NOT, then fail to reject H0.
b. Write a concluding statement:
If you rejected H0��The data is inconsistent with H0 and it provides sufficient evidence to support Ha. If you failed to reject H0��The data does NOT provide sufficient evidence to support Ha. If
value hyp Ha . : >
��
, then it is the area under z curve to the right of calculated z. If
value hyp Ha . : <
��
, then it is the area under z curve to the left of calculated z. If
value hyp Ha . : ��
��
, then it is 2 times the area to right of z (if z is +) OR 2 times the area to the left of z (if z is -). If
value hyp Ha . : >
��
, then it is the area under curve to the right of calculated test statistic. If
value hyp Ha . : <
��
, then it is the area under curve to the left of calculated test statistic. If
value hyp Ha . : ��
��
, then it is 2 times the area to right of test statistic (if test statistic is +) OR 2 times the area to the left of test statistic (if test statistic is -). 1-ProportionZTest
When �� known:
Z-Test
When �� unknown:
T-Test
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