Question

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.)

Answer 1

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