A liquor wholesaler is interested in assessing the effect of...

A liquor wholesaler is interested in assessing the effect of the price of a premium scotch whiskey on the quantity sold. The results in the accompanying table on price, in dollars, and sales, in cases, were obtained from a sample of 8 weeks of sales records. Price 19.2 20.5 19.7 21.3 20.8 19.9 17.8 17.2 Sales 25.4 14.7 18.6 11.4 11.1 15.7 29.2 35.2 Test, at the 5% level against the appropriate one-sided alternative, the null hypothesis that sales do not depend linearly on price for this premium scotch whiskey.

Transcript

00:01 So for this problem, i'm going to assume that since you are asking for excel instructions, that this is to be done all in excel.

00:07 So one thing that i'm going to note here of a bit of peculiarity is that we're explicitly told to test against a one -sided alternative.

00:22 So what i'm going to do is first, just create a little scatter plot of the data, and see, okay, so if there is a linear relation here, it would appear that it should be a negative linear relation.

00:35 So our null hypothesis is that the correlation is equal to zero.

00:42 There's no relation.

00:43 And the alternate hypothesis is that the correlation is less than zero.

00:47 There is a negative correlation.

00:49 So the first thing that i'm going to do here is i'm going to find the critical t value, where the number of degrees of freedom for the t distribution is going to be equal to our number of observations minus one.

01:09 So eight minus one, or we have seven degrees of freedom.

01:13 So i'm going to use excel for finding this t -crit.

01:18 So i'll put in equals t.

01:21 D -i -st the x value, or pardon me, i want t .inv, rather, where i want a probability to the left, if this is at the 0 .05 level, we want 0 .05 to the left, 7 degrees of freedom.

01:35 So we have our critical t value is roughly negative 1 .89.

01:39 So we will reject the null hypothesis if our test statistic is less than roughly negative 1 .89.

01:50 Now our t value is equal to our sample correlation r times n minus 2 divided by 1 minus our sample correlation squared...

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