It is claimed that the variance of the distribution of...

It is claimed that the variance of the distribution of distances in kilometers travelled on 5 litres of fuel by a new car with a diesel engine is less than the variance of the distance travelled by the same model of car equipped with a petrol engine which is known to have a variance of 4.7549 kilometers. Time left 0:43:11 If 11 test runs of the diesel model have a standard deviation of 1.3247 kilometers, can it be concluded (using an appropriate Hypothesis test) at the 0.0200 level of significance, that the variance of the distances travelled by the diesel model is less than that of the petrol model. Assume a Normal Distribution. Instructions Answers to 3 decimal places If a 2 tail test input the Largest Critical Value Answer: The Null Hypothesis Statement = The Alternative Hypothesis Statement = The Critical Value(s) = The Test Value = Is the Null Hypothesis True?0-Accept, 1 - Reject = Is the Claim True?0-Accept, 1 - Reject =

Transcript

00:02 Okay, the question says, right, large sample test of alpha -a -square is going to the variance there when n is greater than or equal to 30, we can test.

00:16 Now i've got this is that the variance is equal to a squared or standard deviation, where it's given that z is going to s plus the standard deviation over the standard deviation divided by the root of 2n there, which is a value of random variables, distribution is approximately the standard normal distribution a that's the question says with reference to example 10 .5 test at the level 0 .05 level of significance whether the standard deviation is equals to 10 years against the alternative that the standard deviation is not equal to 10 years right and b says it is suspected that the variance of the distribution of in kilometers achieved for 5 kilometers of fuel by a new automotive model equipped with the diesel engine is less than the variance of the distribution of distances achieved by the same model equipped with a 6 -cylinder gasoline engine which is known to be variance is equal to 6 .25.

01:27 If 72 test runs in the diesel model have a variance of 4 .5 form for one.

01:38 Then we conclude that at the 0 .05 level of significance that the variance of the distances achieved by the diesel model is less than that of the gasoline model.

01:57 Can we conclude at the 0 .05 level of significance that the variance of the distance achieved by the diesel model is less than that of the gasoline model so that's our p there so let's see how we work on these ones so first of all a right a we are saying that our hypothesis there is is a standard deviation is equal to 10 and then that's the now hypothesis and the alternative says the standard deviation is not equal to 10 there right so and the z how do you get the z z z will be from exercise 10 .5 would be 9 .9 minus which is our s there minus 10 standard deviation there divided by the standard deviation over uh two times n which is hundred right two there and then it gives us 2 .6 9 there and so we are saying the p value is the probability that z is less than 0.

03:17 I mean 2 .6 negative 2 .69, right? plus the probability that z is greater than 2 .69 there.

03:29 And what we are getting is 0 .072 there.

03:34 So hence there is sufficient evidence to conclude that the standard deviation is different from 10.

03:45 So it's not equal to 10.

03:46 So we reject the, there is sufficient evidence to conclude that the standard deviation is different from 10...

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