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

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
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