Question

An automobile manufacturer has given its jeep a 48.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 250 jeeps, they found a mean MPG of 48.9. Assume the population variance is known to be 2.56. A level of significance of 0.01 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Question : An automobile manufacturer has given its jeep a 48.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 250 jeeps, they found a mean MPG of 48.9. Assume the population variance is known to be 2.56. A level of significance of 0.01 will be used. Find the value of the test statistic. Round your answer to two decimal places

Answer :. we have given :  

n = sample size = 250

xbar = sample mean = 48.9

σ2 = known population variance = 2.56 therefore

σ = population standard deviation is = 1.6

μ = population mean = 48.7

alpha = 0.01 level of significance .

Step 1 ) statement of the null and alternative Hypothesis :

Ho : μ = 48.7 vs H1 : μ ≠ 48.7

Step 2) test statistics : z test

here all condtion of the z test statistics satisfy hence it used ( n >30 , and known variance)

z = ( xbar -  μ ) / ( σ / sqrt(n))

z = ( 48.9 - 48.7 ) / ( 1.6 / 15.8113)

z = ( 0.2 ) / 0.1011

z = 1.9764   ≈ 1.97

## Step 3) alpha = 0.01 level of significance

## Step 4) critical value

= z ( alpha /2) = 2.58 ( from table )

## Step 5) Decision :

we reject Ho at given level of significance if z stat value is greater than z critical value

here z stat value is less than z critical value here we fail to reject Ho at given level of significance .

## Step 6) Conclusion :

there is not sufficient evidence to conclude that population mean is not equl to the 48.7 .at alpha is 0.01

that is population mean is equal to the 48.7 MPG