Transcript Significance Test for Two Means

Warm-up
9.3 and 9.4 C.I and Inference Test of Two Means
1. A doctor wishes to compare the resting heart rates of his younger
patients (younger than 30 years old) versus his older patients. Which of
the following graphical displays is inappropriate.
A. Back-to-back stemplot B. Parallel boxplots
C. Side by side histograms D. Scatterplots
E. All of the above are appropriate.
2. Consider n pairs of numbers. Suppose x  4 , s x  3, y  2 and s y  5 .
Of the following which could be the least squares line?
A. y = 2 + x B. y = -6 + 2x C. y = -10 + 3x D. y = 5/3 – x
E. y = 6 - x
H.W. Answers to 8.4 D# 45
S.E. for n = 10 is 0.071
S.E. for n = 50 is 0.158
9.3 C.I. and Significance Test for Two Means
• Comparing means is not that different from comparing two
proportions.
• Remember with means t* is used instead of z*
• To find t* use the table NOT InvNorm.


SD y 1  y 2 

Var ( y 1 )  Var ( y 2 ) 
 
 1
 n
1

2

 
   2

 n
2






2
SD ( y 1 )  SD ( y 2 )
2
1
2

n1
2
2
2

n2
• Confidence Interval ( y 1  y 2 )  t *  SE ( y 1  y 2 )
• t* for degrees of freedom (degrees of freedom is not easy
to find)
Finding the Confidence Interval for a difference of 2 Means
Judging from the boxplot, the generic batteries seem to
have lasted about 20 minutes longer than the brand-name
batteries. Before we change our buying habits, what should
we expect to happen with the next batteries we buy?
6 sets of AA batteries were randomized
and tested for duration length.
Calculate the 95% C.I. to find the
true difference between the two
means.
Significance Test Difference Between Two Means
It is a common believe that women tend to live longer than
men. Random samples from death records for mean and
women in Montgomery County were taken, and age at the
time was recorded. The average age of the 48 males was
68.33 with a standard deviation of 12.49 years, while the
average age of the 40 females was 78.7 years with a
standard deviation of 16.43 years. Do women in this county
tend to live longer than men? Give the appropriate statistical
evidence. STAT => TESTS=>2-SampTTest
Ho:  F   M  0
HA:  F   M  0
Direction for the rest of the block
• Finish the notes, both the confidence interval AND the
significance test.
• When you finish organize your notes and show them to me.
10.1, 10.2, 10.3, Ch.11 Day 1, Ch. 11 Day 2, 8.3 & 8.4, 9.3 &
9.4 (7 notes with warm-ups 14 pts each 7 x 14 = 98)
*****Don’t bring me any notes that are not fillled in *****
• Once you show me your notes start on the multiple choice
for the practice cumulative tests.
• Remember to return formula sheets AND the cumulative
practice test if you borrowed the class set!
• REMEMBER the cumulative test will be timed!
2minutes per multiple choice (2* 12 = 24minutes!)
15 minutes per free response ( 15* 3 = 45 minutes!) = 70
Significance Test for Two Means
t is about 3.28; p-value is 0.0008.
I reject the null hypothesis that there is no difference
between the two means. If there was no difference there
is only 8 out of 10,000 samples that would have the same
mean difference or more extreme. Women in Montgomery
County tend to live longer than men.
Complete the multiple choice for h.w.
We will review the answers, next block.
You will be given time to complete the free-response.