Two Sample t-tests and t-intervals

Resting pulse rates for a random sample of 26 smokers had a mean of 80 beats per minute (bpm) and a standard deviation of 5 bpm. Among 32 randomly chosen nonsmokers, the mean and standard deviation were 74 and 6 bpm. Both sets of data were roughly symmetric and had no outliers. Is there evidence of a difference in mean pulse rate between smokers and non-smokers? How big?

There is no difference between the mean resting pulse rate for smokers and non-smokers.

There is a difference between the mean resting pulse rate for smokers and non-smokers

0 : 0S NSH

: 0A S NSH

1. Randomization: Stated as random samples2. Independence: The groups are

independent of each other3. Nearly Normal: Both sets of data were

stated as roughly symmetric and unimodal

All conditions have been met to use Student’s t-Model for a two-sample t-test.

26Sn 0.05 6NSs

80Sx 5Ss 32NSn 74NSx

55.95t 2 2

80 74

5 626 32

S NSx x

2 2S NS

S NS

s sn n

4.15

55.95 56df

P Value 55.952 ( 4.15)P t 0.00011

Since the P-Value is less than alpha (0.00011<0.05) we reject the null hypothesis. There is statistically significant evidence that there is a difference in the mean resting pulse rate of smokers and non-smokers.

Same Conditions

We are 95% confident that the average resting pulse rate for smokers is between 3.1 and 8.9 beats per minute higher than for non-smokers.

2 2

: S NSS NS df

S NS

s sCI x x t

n n

2 25 6

80 74 2.00326 32

(3.1,8.89)

Here are the saturated fat content (in grams) for several pizzas sold by two national chains. Do the two pizza chains have significantly different mean saturated fat contents?

Brand D17 12 10 8 8 10 10 5 16 168 12 15 7 11 11 13 13 11 12

Brand PJ

6 7 11 9 4 4 7 9    11 3 4 5 8 5 5      

There is no difference in the mean saturated fat contents of the two pizza chains

There is a difference in the mean saturated fat contents of the two pizza chains

0 : 0D PJH

: 0A D PJH

1. Randomization: Not stated as random, we will assume that the samples are representative of all pizzas for the two chains

2. Independence: The pizza chains are independent of each other

3. Nearly Normal: Normal probability plots of both graphs are approximately linear.

All conditions have been met to use Student’s

t-Model for a two-sample t-test.

20Dn 0.05 2.588PJs

11.25Dx 3.193Ds 15PJn 6.53PJx

32.8t 2 2

11.25 6.53

3.193 2.58820 15

D PJx x

22PJD

D PJ

ss

n n

4.823

32.8 33df

P Value 32.82 ( 4.823)P t 0.00003

Since the P-Value is less than alpha (0.00003<0.05) we reject the null hypothesis. There is statistically significant evidence that there is a difference in the mean saturated fat content between the two pizza chains.