A car manufacturer claims that with the new collapsible...

A car manufacturer claims that with the new collapsible bumper system, the mean body repair cost for the damage sustained in a collision impact of 15 miles per hour does not exceed $400. To test the validity of this claim, 6 cars are crashed into a barrier at 15 miles per hour and their repair costs recorded. The mean and standard deviation from these crashes are found to be $458 and $48, respectively. At the = .05 significance level, test data the manufacturer’s claim . Assume the sample was taken from a normal population.

Transcript

00:01 So our question says that a car manufacturer claims that the new collapsible bumper system, with the new collapsible bumper system rather, the mean body repair cost for the damage sustained in a collision impact of 15 miles per hour does not exceed $400.

00:16 So to test the validity of this claim, six cars are crashed into a barrier at 15 miles per hour and the repair cost was recorded.

00:24 So the main and standard division from these crashes are found to be $458 and $48 .48.

00:30 Respectively so at 5 % level of significant test manufacturer's claim assumed the sample was taken from a normal population so according to the manufacturer the population we knew is actually cost to 400 dollar a sample of six cars were crashed the sample mean of amount spent was actually for 58 dollars and the sample standard division else was actually 48 so let's go into the question again it says a car manufacturer claims that with the new collapsible collapseable bumper system rather the mean body repair cost for the damage sustained in a collision impact of 15 miles per hour does not exceed 400 so that means our h -not is that mule is at most 400 dollar but the alternative hypothesis is that m is going to be greater than 400 so after stating the null and alternative hypothesis the next step is for us to get our test statistics and test statistics can either be a z test or a t test depending on the data sets that we have from our distribution.

01:34 As you can see, we have our sample size which is equal to 6.

01:37 We don't have the value of the population standard division.

01:40 Instead, we are making use of the value of the sample standard division.

01:43 This simply tells us that we are going to be using a t test as our test statistics.

01:48 So we have t is equals to x bar minus m divided by s divided by this count of n.

01:53 So we have this to be cost to 458 minus 400 divided by our s.

01:59 Is actually 48 divided by the square root of 6.

02:02 So we have this to be 58 divided by.

02:05 So using our calculator, 48 divided by the square root of 6, we have our answer to be 19 .596.

02:14 And when we do the math, 58 divided by 19 .596, the answer is at 2 .959.

02:22 So our test statistics is 2 .95 in a rather...