Question

Ford Motor Company publishes that the average price of a new Edge is $38,900, with a standard deviation of $1300. You feel that the average price is more than the company says so you check the price stickers on 32 cars and find the average cost to be $39,400. At a=0.05 are you correct?

Answer 1

Solution:

Given: Ford Motor Company publishes that the average price of a new Edge is $38,900, with a standard deviation of $1300.

That is: Mean = and standard deviation =

Claim: the average price is more than the company

Sample size = n = 32

Sample mean =

Level of significance =

Step 1) State H0 and H1:

Vs

Step 2) Find test statistic.

Since sample size n = 32 > 30 , we can assume sampling distribution of sample means is approximately Normal and hence we use z test statistic.

Step 3) Find z critical value.

Since is > type, this is right tailed test.

Thus find an area =

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_critical = 1.645

Step 4) Decision rule:

Reject H0, if z test statistic value > z critical value = 1.645 , otherwise we fail to reject H0.

Since z test statistic value = 2.18 > z critical value = 1.645, we reject H0.

Step 5) Conclusion:

Since we have rejected H0, there is sufficient evidence to conclude that: the average price is more than the company