Answer:
A
The test statistics is [tex]t = -1.7[/tex]
B
The Null and Alternative hypothesis are
[tex]H_o : \mu = 47.2[/tex] and [tex]H_a : \mu \ne 47.2[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 47.2 miles/gallon(MPG)[/tex]
The sample size is [tex]n = 250 \ van[/tex]
The sample mean is [tex]\= x = 47.0[/tex]
The sample standard deviation is [tex]\sigma = 1.9[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
Given that the value which the manufacturer gave the automobile is 47.2 and it is believed that this is not correct, then
The Null Hypothesis is
[tex]H_o : \mu = 47.2[/tex]
The alternative Hypothesis is
[tex]H_a : \mu \ne 47.2[/tex]
The test statistics can be mathematically evaluated as
[tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }[/tex]
[tex]t = -1.7[/tex]
