Warm-up9.3 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

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

.5and2,3,4 yx sysx

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.

• Confidence Interval• t* for degrees of freedom (degrees of freedom is not easy

to find)

2

22

1

21

2

2

2

2

1

1

22

212121 )()()()(

nnnn

ySDySDyVaryVaryySD

)(*)( 2121 yySEtyy

Finding the Confidence Interval for a difference of 2 MeansJudging from the boxplot, the generic batteries seem tohave lasted about 20 minutes longer than the brand-namebatteries. Before we change our buying habits, what shouldwe expect to happen with the next batteries we buy?

6 sets of AA batteries were randomizedand tested for duration length.

Calculate the 95% C.I. to find the true difference between the twomeans.

Significance Test Difference Between Two MeansIt is a common believe that women tend to live longer thanmen. Random samples from death records for mean andwomen in Montgomery County were taken, and age at thetime was recorded. The average age of the 48 males was68.33 with a standard deviation of 12.49 years, while theaverage age of the 40 females was 78.7 years with astandard deviation of 16.43 years. Do women in this countytend to live longer than men? Give the appropriate statisticalevidence. STAT => TESTS=>2-SampTTestHo:

HA: 0

0

MF

MF

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 differencebetween the two means. If there was no difference thereis only 8 out of 10,000 samples that would have the samemean difference or more extreme. Women in MontgomeryCounty 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.