Question

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

Use the given data set of x and y values to answer the following questions. x-values 1 1 1 2 2 2 3 3 3 9 y-values 8 9 10 8 9 10 8 9 10 2

(a) Use StatCrunch to find the regression equation, ˆy = b0 + b1x and the sample correlation coefficient, r. Round all computations to three decimal places as needed.

(b) When α = 0.01, the critical values are −0.765 and 0.765. Is there a correlation between x and y?

(c) Find the best-predicted value y-value when x = 5. Round to the nearest tenth as needed.

Answer 1

The regression output is as follows

Null Hypothesis : There is no relation between x and y

Atlernate Hypothesis : There is correlation between x and y

F-test statistic from ANOVA table is 27.52739. UsuallyF-statistic is used for whole regression. but sometimes t-statistic of the x-variable is also taken which is -5.24665 here

p-value from ANOVa tabe is 0.000776984 (here we can also take the p-value fromx-variable which is same)

Since our p-value is less than alpha value of 0.05, we reject the null hypothesis

So the conclusion is there is correlation between x and y

Question (a)

The regression equation is =  10.677 + (-0.880) * x

Sample correlation coefficent r from the regression stastics multiple R = 0.880 rounded to 3 decimal places

Question (b)

Here the ciritcal values are −0.765 and 0.765. The t-test statistic of the x variable is -5.247 at = 0.01

The t-test statistic falls in the critical region because the critical region is from negative infinity to -0.765 and from 0.765 to positive infinity

So We reject the Null Hypothesis

Hence there is a correlation between x and y

Question (c)

The regression equation is =  10.677 + (-0.880) * x

=  10.677 + (-0.880) * 5

   = 10.677 - 4.4

   = 6.277

The besr predicted value of y = 6.3