Transcript Section 7.4, Completed

MATH 2311
Section 7.4
Confidence Interval for a Population Mean
So, what is t*?
How do we find critical values for a tdistribution?
Look at the online text book, under appendices.
Degrees of freedom are on the left and the top end (1-confidence
level/2) are given at the top.
Using R-Studio to find t* values:
The command is qt(1.##/2,df)
If you are using a confidence level of 90% with 20 degrees of freedom,
you would use the command:
qt(1.90/2,20)
In the TI 83/84 Calculators, Select 2nd, DISTR, and select invT.
invT(1.90/2,20)
Assumptions:
Examples:
Examples:
Look at the following example:
The effect of exercise on the amount of lactic acid in the blood was
examined in an article for an exercise and sport magazine. Eight males
were selected at random from those attending a week-long training
camp. Blood lactate levels were measured before and after playing
three games of racquetball, as shown in the accompanying table. Use
this data to estimate the mean increase in blood lactate level using a
95% confidence interval.
Values to cut and paste:
assign(“before”,c(13,20,17,13,13,16,15,16))
assign(“after”,c(18,37,40,35,30,20,33,19))
t-score table:
t-score table:
Since n = 8, we are going to use the
value for n – 1 = 7 degrees of
freedom.
Since we want a confidence level of
95%, we will use an “Upper Tail
Probability” of (1 – 0.95)/2 = 0.025.
This is to account for only using one
tail end of our graph, rather than 2.
Our t* value will be 2.3646.
Confidence Interval Calculation:
Interpretation of the Confidence Interval:
Example:
A 95% confidence interval for the mean of a population is to be
constructed and must be accurate to within 0.3 unit. A preliminary
sample standard deviation is 2.9. Find the he smallest sample size n
that provides the desired accuracy.
Popper 17:
A group of 10 students are comparing exam scores for a test they recently took.
Based on these results, you want to find out, with 90% confidence, what range of
grades you can expect to receive.
Exam Scores: 70, 75, 80, 87, 90, 90, 93, 94, 96, 100
1. What is the sample mean?
a. 90
b. 87.5
c. 80
d. 91.6
2. What is the sample standard deviation?
a. 9.62
b. 92.5
c. 5.65
d. 13.83
3. What is the t* value that can be used here?
a. 1.3722
b. 1.3968
c. 1.8331
d. 1.6449
4. What is the margin of error?
a. 5.58
b. 5.00
c. 4.03
d. 6.12
5. What is the confidence interval?
a. [70,100]
b. [87.5, 100]
c. [85.67, 89.33]
d. [81.92, 93.08]