What is the value of the sample test statistic?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

What is the value of the sample test statistic? (Round your answer to three decimal places.)

The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of
the cars at the time of replacement were (in months):
25 48 47 48
53 46
30 51 42
52
n USE SALT
(i) Use your calculator to calculate the mean age of a car when the fuel injection system fails x and standard deviation s. (Round your answers to four decimal places.)
X = 44.2
months
s =9.4257
months
(ii) Test the claim that the fuel injection system lasts less than an average of 48 months before needing replacement. Use a 5% level of significance.
What are we testing in this problem?
O single proportion
O single mean
(a) What is the level of significance?
0.05
State the null and alternate hypotheses.
О Но: и 3D 48;B Hi: и < 48
О Но: и3D 48%;B Hi: и > 48
O Ho: p = 48; H1: p < 48
О Но: и 3D 48; Hi: и + 48
О Но: р%3D 48; Hi: р# 48
О Но: р %3D 48; Hi: р > 48
(b) What sampling distribution will you use? What assumptions are you making?
O The Student's t, since we assume that x has a normal distribution with unknown o.
O The standard normal, since we assume that x has a normal distribution with known o.
O The standard normal, since we assume that x has a normal distribution with unknown o.
O The Student's t, since we assume that x has a normal distribution with known o.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
|-1.28
Transcribed Image Text:The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of the cars at the time of replacement were (in months): 25 48 47 48 53 46 30 51 42 52 n USE SALT (i) Use your calculator to calculate the mean age of a car when the fuel injection system fails x and standard deviation s. (Round your answers to four decimal places.) X = 44.2 months s =9.4257 months (ii) Test the claim that the fuel injection system lasts less than an average of 48 months before needing replacement. Use a 5% level of significance. What are we testing in this problem? O single proportion O single mean (a) What is the level of significance? 0.05 State the null and alternate hypotheses. О Но: и 3D 48;B Hi: и < 48 О Но: и3D 48%;B Hi: и > 48 O Ho: p = 48; H1: p < 48 О Но: и 3D 48; Hi: и + 48 О Но: р%3D 48; Hi: р# 48 О Но: р %3D 48; Hi: р > 48 (b) What sampling distribution will you use? What assumptions are you making? O The Student's t, since we assume that x has a normal distribution with unknown o. O The standard normal, since we assume that x has a normal distribution with known o. O The standard normal, since we assume that x has a normal distribution with unknown o. O The Student's t, since we assume that x has a normal distribution with known o. What is the value of the sample test statistic? (Round your answer to three decimal places.) |-1.28
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman