Question 1 records of 40 used passenger cars and 40 used...

Question 1 Records of 40 used passenger cars and 40 used pickup trucks (none used commercially) were randomly selected to investigate whether there was any difference in the mean time in years that they were kept by the original owner before being sold. For cars the mean was 5.3 years with standard deviation 2.2 years. For pickup trucks the mean was 7.1 years with standard deviation 3.0 years. Test using the 1% level of significance. For each hypothesis test, you must include the following to get full credit: H0: ______ Ha: ____ In words, define the random variable. The distribution to use for the test is _____________. Calculate the test statistic using your data. Draw a graph and label it appropriately. Calculate the p-value. Do you reject or not reject the null hypothesis? Why? Write a clear conclusion using a complete sentence.

Transcript

00:01 But let's see, yep, just plain on three.

00:02 Standard deviation for trucks is three years.

00:06 And we want to know if there's a difference between the amount of time that people keep a car or a truck.

00:11 So our null hypothesis is that the mean number of years that a car is held is equal to the main number of years that a truck is held.

00:19 Or that the difference, and again, it doesn't matter which way i subtract, but i'll just do it this way, that the difference between them is zero.

00:27 And alternately that they're not equal, meaning that the difference between the two does not equal zero.

00:38 And so graphically, basically our random variable is we're going to be taking an x bar from a car and an x bar from a t, and we're going to look at the distribution of subtracting these two.

00:54 And so our sampling distribution is looking at the difference between these.

00:59 And we're assuming the difference is zero.

01:02 And we can see from our sample that we're actually getting a difference that's negative, like negative 1 .8.

01:08 So we're getting a difference that's down here.

01:10 And so we want to know how likely it is to get a difference down here of negative 1 .8 or up here.

01:17 So let's go.

01:18 So what is the probability of sampling and getting the difference between these x.

01:24 Bars being less than or equal to that what we got, which was the 5 .3 minus the 7 .1.

01:33 Now we can change that.

01:35 And because it's a two -tail test, we will actually take this and and that end and add them together.

01:41 So let's change it to a test statistic.

01:44 Our test statistic is a t value.

01:46 Now, we're going to conservatively use 39 degrees of freedom, the less one number less than the smaller sample size.

01:56 And there's a formula that we can use to find that.

01:58 We can use software to find it, and maybe we'll do that and see what it says...

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