Unit 6
By Vincent Giovagnoli, Courtney Beck, & Ayla Odins
Chapter 23
• In this chapter we use the t test to find our true mean of the data given.
• With the t test we find out if our null hypothesis is retained or rejected.
• If we are trying to find the confidence interval we have to use inverse t.
Example
• Textbooks authors must be careful that the reading level of their book is
appropriate for the target audience, Some methods of assessing reading level
require estimating the average word length. We’ve randomly chosen 20 words
from randomly selected page in Stats: Modeling the World and counted the
number of letters in each word:
• 5, 5, 2, 11, 1, 5, 3, 8, 5, 4, 7, 2, 9, 4, 8, 10, 4, 5, 6, 6
Example Cont.
• Suppose that our editor was hoping that the book would have a mean word
length of 6.5 letters. Does this sample indicate that the authors failed to meet
this goal? Test an appropriate hypothesis and state your conclusion.
• H : mean = 6.5
• H : mean ≠ 6.5
• Type in all the data and put it in the calculator. If it is uni-model,
O
A
symmetrical, and follows the normal curve.
• Independent, Random, <10%, & Nearly Norm
Example Cont.
• We find the degree of freedom by subtracting the number of data points(20)
by 1. (20-1=19) 19 = degree of freedom
•
•
•
•
•
Standard Error = Standard deviation/ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠
2.69/√20 = .6
T19(6.5, .6)
T=(Actual mean - null hyp. Mean)/Standard Error
T= (5.5-6.5)/.6 = -1.67
Example Cont.
• T cdf (-∞,-1.67,19) = .0557
• . 0557 x 2 = .11
• We retain the null because of the high P-value. This means that the mean
word length is 6.5
Chapter 24
• This chapter has to do with analyzing two sets of data.
• We use the 2 sample t test in our calculator to work out our real world data
and figure out if our hypothesis is true.
• Also, we use 2 sample t interval to figure out confidence intervals with our
data.
Example
• A random sample of 13 men and 19 women in a college class reported their
grade point averages(GPAs).
s
ȳ
Men
2.898
0.583
• This is the summary of the data: Women
3.330
0.395
• A woman in the class says that she believes that college women tend to have
higher GPAs than college men. Does this sample support her claim? Test an
appropriate hypothesis and state your conclusion.
Example Cont.
• H:m –m =0
• H:m –m <0
• Type in all the data and put it in the calculator. If it is uni-model,
o
1
2
A
1
2
symmetrical, and follows the normal curve.
• Independent, Random, >10%, & a nearly normal curve.
• T (0,.19)
20
Example Cont.
• Standard Error =
•
.5832
13
+
.3952
19
𝑆𝐷2
√
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠
+
𝑆𝐷2
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠
= .185
• 2 sample t test (2.89, 0.583,13,3.33,0.395,19)=.015
• With a low P-value of .015 we reject the null, which means we found data to
suggest that men have lower GPAs than women.
Chapter 25
• This chapter helps us analyze two sets of data.
• Like chapter 23, we use t cdf in our calculator.
Example
• Parents of students have had bad experiences with Statistics courses and pass
on to their anxieties to their children. To test whether actually taking AP
Statistics decreases students’ anxieties about Statistics, an AP Statistics
instructor gave a test to rate student anxiety at the beginning and end of his
course. Anxiety levels were measured on a scale of 0-1-. Here are the data for
16 randomly chosen students from a class of 180 students.
Pre-course anxiety level
7
6
9
5
6
7
5
7
6
4
3
2
1
3
4
2
Post-course anxiety level
4
3
7
3
4
5
4
6
5
3
2
2
1
3
4
3
Difference (Post – Pre)
-3 -3
-2
-2
-2
-2
-1
-1
-1
-1
-1
0
0
0
0
1
Example Cont.
• H :m –m =0
• H:m –m <0
• We have to type the data points into our calculator to see if the histogram
O
1
2
A
1
2
follows the normal model.
• Independent, Random, Nearly Normal Histogram, and <10%
1.15
• Standard Error = √16 = .29
Example Cont.
• T (0,.29)
15
• T=
−1.125 −0
.29
= -3.88
• T cdf (-∞, -3.88,15) = .00074
• With a low P-value we reject the null which means students that take AP
Stats have less anxiety.