In: Statistics and Probability
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): 27 46 49 48 53 46 30 51 42 52
What is the value of the sample test statistic? (Round your answer to three decimal places.)
The sample standard is = 5.7588
x
/n = (27 +46+ 49 +48+ 53 +46 +30 +51 +42+ 52 / 10)
= 444/ 10
= 44.4
The sample mean is 44
Sample standard deviation is s
s =
1/(n-1)
(x -
)2
= 1/9
(11 - 44)2+ (15 - 44)2+ (17 -
44)2+ (20- 44 )2 +( 21 - 44 )2+
(22 - 44)2 + (27 - 44 )2 +( 21 - 44
)2+ (22 - 44)2 + (27 - 44 )2 )
=
1/ 9 (289 +4+25+16+81+4+196+49+4+64 )
=
732/9
=
81.3333
= 9.02
Sample standard deviation is s = 9.02
Solution :
=
48
= 44
s = 19.02
n = 10
Test statistic = t
= (
-
) /
/
n
= (44 - 48) / 9.02 /
10
= −1.402
The value of the sample test statistic = −1.402