Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion
There is no sufficient evidence to conclude that the vans underperform the manufacturer's MPG rating
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 46.4 \ miles/gallon[/tex]
The sample size is n = 140
The sample mean is [tex]\= x = 46.0[/tex]
The standard deviation is [tex]\sigma = 2.6[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
The null hypothesis is [tex]H_o : \mu = 46.4[/tex]
The alternative hypothesis is [tex]H_a : \mu < 46.4[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 46 - 46.4 }{ \frac{ 2.6 }{\sqrt{140} } }[/tex]
=> [tex]t = -1.8203[/tex]
From the z table the area under the normal curve to the left corresponding to
-1.8203 is
[tex]P(Z < -1.820 ) = 0.03438[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(Z < -1.820 ) = 0.03438[/tex]
From the value obtained we see that the p-value > [tex]\alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion
There is no sufficient evidence to conclude that the vans underperform the manufacturer's MPG rating
