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a manufacturer claims that one of its new cars having a highway fuel efficiency average of 30 miles per gallon. A consumer interest group would like to test whether there is any statistical evidence that the manufacturer is over stating the MPG. A sample of 25 cars of this brand resulted in a sample mean highway mileage rating of 29.5 MPG and a standard deviation of 1.8 MPG. State the null and alternative hypothesis needed to conduct this test. What test statistic should be used and why? Should any assumption be made about the distribution of MPG? What conclusion can be drawn from the sample results? Test at 0.05 level of significance.

Respuesta :

Answer: We reject the null hypothesis.

Step-by-step explanation:

Since we have given that

Null and alternate hypothesis are

[tex]H_0:\mu =30\\\\H_1:\mu \neq 30[/tex]

n = 25 and α = 0.05

Degrees of freedom would be

[tex]n-1\\\\=25-1\\\\=24[/tex]

Using t-table, we get that

[tex]t_{0.05,24}=2.0638[/tex]

[tex]\bar{X}=29.5\\\\s=1.8\\\\n=25[/tex]

[tex]t=\dfrac{\bar{X}-\mu}{\dfrac{s}{\sqrt{n}}}\\\\t=\dfrac{29.5-30}{\dfrac{1.8}{\sqrt{25}}}\\\\t=\dfrac{-0.5}{0.36}\\\\t=-1.39[/tex]

Since -1.39<2.0638

So, we reject the null hypothesis.

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