An automobile manufacturer has given its car a 52.6 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 250 cars, they found a mean MPG of 52.8. Assume the population standard deviation is known to be 1.6. A level of significance of 0.05 will be used. State the null and alternative hypotheses.

Null hypothesis:  

Alternative hypothesis:  

Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.

Step-by-step explanation:

Information provided

represent the sample mean  for the MPG of the cars

represent the population standard deviation

sample size  of cars

represent the value that we want to test

represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

represent the p value for the test

Hypothesis

We need to conduct a hypothesis in order to check if the true mean of MPG is different from 52.6 MPG, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

Since we know the population deviation the statistic is given by:

 (1)  

Calculate the statistic

Replacing we have this:

Decision

Since is a two tailed test the p value would be:  

Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.

1

step-by-step explanation:

you are throwing one dart

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.