Inferences About Means Continued OneSample t Test for a Mean State hypotheses Check conditions amp Model Mechanics Conclusion Confidence Interval when appropriate 95 if not specified otherwise ID: 592785
Download Presentation The PPT/PDF document "Chapter 23 part 2" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Chapter 23 part 2
Inferences About Means, ContinuedSlide2
One-Sample
t
-Test for a Mean
State hypotheses
Check conditions & Model
Mechanics
Conclusion
Confidence Interval when appropriate (95% if not specified otherwise)Slide3
A coffee machine dispenses coffee into paper cups. You’re supposed to get 10 ounces of coffee, but the amount varies slightly from cup to cup. Here are the amounts measured in a random sample of 20 cups. Is there evidence that the machine is shortchanging customers?
9.9
9.7
10.0
10.19.99.69.89.810.09.59.710.19.99.610.29.810.09.99.59.9
*Put these values in L1 in your calculator.Slide4
1) State the hypotheses.
Slide5
2) Check conditions & model.
Random sample
Cups are independent
Meets 10% Condition (20 is less than 10% of all cups)
Distribution needs to be roughly unimodal and symmetric (Nearly Normal Condition) Perform a one-sample t-test with 19 degrees of freedom.Slide6
3) Mechanics
n = 20
df
= 20-1 = 19
s = 0.199
P-value =
This comes from the calculator:
2
nd
VARS
#6
tcdf
(-99, -3.49, 19)Slide7
4) Conclusion
Such a small P-value makes it unlikely that the low sample mean resulted from sampling error, so we reject the null hypothesis. There is sufficient evidence to conclude that the mean amount of coffee dispensed by this machine is less than the stated 10 fluid ounces.Slide8
5) Confidence Interval
The conditions have been met, so we can create a one-sample t-interval with 95% confidence.
Sample mean
(critical value t)(standard error)
We are 95% confident that the machine dispenses an average of between 9.75 and 9.94 ounces of coffee per cup.Slide9
Example – Turn this in today!
A professor at a large university believes that students take an average of 15 credit hours per term. A random sample of 24 students in her class of 250 students reported the following number of credit hours that they were taking:
12
13
1414151515161616161617171718181818
19
19
19
20
21
Does this sample indicate that students are taking more credit hours than the professor believes? Test an appropriate hypothesis and state your conclusion.
Find a 95% confidence interval for the number of credit hours taken by the students in the professor’s class, and interpret the interval.Slide10
Today’s Assignment:
Be sure to turn in the practice problem.
Add
to HW:
p. 554 #5-8, 30