Stat 101 – Lecture 31
Inference for µ
• What is the mean heart rate for all
young adults?
• Use the sample mean heart rate, y ,
to make inferences about the
population mean heart rate, µ .
1
Sample Data
• Random sample of n = 25 young
adults.
• Heart rate – beats per minute
70, 74, 75, 78, 74, 64, 70, 78, 81, 73
82, 75, 71, 79, 73, 79, 85, 79, 71, 65
70, 69, 76, 77, 66
2
Summary of Data
• n = 25
• y = 74.16 beats
• s = 5.375 beats
• SE ( y ) =
s
= 1.075 beats
n
3
Stat 101 – Lecture 31
Conditions
• Randomization condition: met.
• 10% condition: met.
• Nearly normal condition: met.
4
Normal Quantile Plot
3
.99
2
.95
.90
1
.75
0
.50
.25
-1
.10
.05
-2
.01
-3
6
4
Count
8
2
60
65
70
75
80
85
90
Heart rate
5
Nearly Normal Condition
• Normal quantile plot – data follows
straight line for a normal model.
• Box plot – symmetric.
• Histogram – unimodal and
symmetric.
6
Stat 101 – Lecture 31
Confidence Interval for µ
y − tn*−1SE ( y ) to y + tn*−1SE ( y )
tn*−1 is from Table T
SE( y ) =
s
n
7
Table T
df
1
2
3
4
M
2.064
24
Confidence Levels 80%
90%
95%
98%
99%
8
Confidence Interval for µ
y − tn*−1SE ( y ) to y + tn*−1SE ( y )
74.16 ± 2.064(1.075)
74.16 − 2.22 to 74.16 + 2.22
71.94 beats to 76.38 beats
9
Stat 101 – Lecture 31
Interpretation
• We are 95% confident that the
population mean heart rate of
young adults is between
71.94 beats/min and 76.38 beats/min
10
Interpretation
• Plausible values for the population
mean.
• 95% of intervals produced using
random samples will contain the
population mean.
11
JMP:Analyze – Distribution
Mean
Std Dev
Std Err Mean
Upper 95% Mean
Lower 95% Mean
N
74.16
5.375
1.075
76.38
71.94
25
12