CI and Testing to compare Means
NEW TYPE OF QUESTION
Test whether men at AASU have a mean travel distance that is greater than the mean travel distance for women. Use a = .01. Collect data on 3 men and 3 women. Ho: mmen = mwomen Ha: mmen > mwomen
Note: these are really too small samples.
THEORY:
______is a t-score
when you compare it to a t-value in the t-table A-53
your df =
______
EEEKK!! Let XL do it.
This number is always between
((Smallest n) –1) and (the sum of the n’s – 2)
Let’s use the steps I proposed last time…..
1.Read the Problem
A. Ha: is < or > then it is a one-tail test
Ha: is a not equal to sign then it is a two-tail test
B. Note what a value is shown in the problem
C. Is the data continuous? You will use the t-tables
D. Work with your data.
Find the sample means and look around for s the standard deviation of the data
E. Calculate df the degrees of freedom by computing
n – 1, i.e. the sample size = number of pieces of data and subtract 1 from it OR
crazy df if comparing means
(approximately <min of n’s-1> to <sum of n’s-2>
2. compute a t-score
( - m)
------where m is the ‘guessed’ mean
mentioned in the hypotheses and s was
s / given to you in the problem
or for this new situation
/
3. go to the t-tables in A-53
A.Look for 2-tail or one-tail
B. Look for a...... so now you know which column
C. Find the correct row by using your df
D. Pluck off your t-value
E. Put a negative in front of your t-value if there is a < in your Ha hypothesis
4.COMPARE
A.If Ha is < and your t-score < - t-value then “go with”
Ha
B. If Ha is > and your t-score > - t-value then “go with”
Ha
C. If Ha is not equal to sign then if either A. or B. is true then “go with” Ha.
The t-tables are found in text
Upper tail probability
df .10 .05 .025 .01…
1 3.078 6.314 12.706 31.821….
2 1.886 2.920 4.303 9.925 ….
3 1.638 2.353 3.182 4.541 …
. . . . ….
45
50 1.299 1.676 2.009 2.403
. . . . .
1000 1.282 1.645 1.960 2.326
------
80% 90% 95% 98%
Confidence level
Now let’s instead build a 90% confidence interval for the difference in the mean number of miles traveled to campus by men and women.
+- t*
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