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An automobile manufacturer claims that its jeep has a 37.0 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 140 jeeps, they found a mean MPG of 37.2. Assume the variance is known to be 1.69. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Respuesta :

Answer:

The value of the test statistic is 1.82    

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 37.0 MPG

Sample mean, [tex]\bar{x}[/tex] = 37.2 MPG

Sample size, n = 140

Alpha, α = 0.05

Population variance,

[tex]\sigma^2 = 1.69\\\Rightarrow \sigma = 1.3[/tex]

Formula: for z-statistic:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{37.2 - 37.0}{\frac{1.3}{\sqrt{140}} } = 1.82[/tex]

Thus, the value of the test statistic is 1.82

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