A firm that prints automobile bumper stickers conducts a study to investigate th

Question

A firm that prints automobile bumper stickers conducts a study to investigate the relation between the direct cost of producing an order of bumper stickers (TOTCOST) and the number of stickers(Runsize, in 1,000s of stickers) in a particular order. Data given below:

a. Test the hypothesis H0: = 0 using a t-test with = 0.05

b. Determine the P-value for this test and interpret its value

c. Compute the value of the F statistic and the associated p value

d. How do the p-values for this F statistic and the t test compare. Why should this relation hold?

2.6 5.0 10.0 2.0 .8 4.0 2.5 0.8 RunSize TOTCOST 230 341 629 187 159 1.0 327 206 124 155 147 RunSize TOTCOST 209 247 2.0 3.0 5 5.0 20.0 5.0 2.0 1.0 1.5 135 125 366 1146 339 20850 179 RunSize TOTCOST 1.0 143 131 6 2.0 219 1.5 3.0 6.52.2 1.0 171 258 415 226 159 128 155

Explanation / Answer

(a)  H0: = 0 Ha : 0

Here p - value is for the RunSize is 0.000 < 0.05 so we can reject the null hypothesis and can claim that there is significant linear relationship.

(b) P - value = Pr(T > 88.53) = 0.00000 so we shall reject the null hypothesis.

(c) F- stat = 7837.26

and associate p - value = 0.0000

that means there is atleast one of the coefficient of independent variable is significant here.

(d) These p - values are under significane level. F test tests the overall significance of the regression model.  Specifically, they test the null hypothesis that all of the regression coefficients are equal to zero.  This tests the full model against a model with no variables and with the estimate of the dependent variable being the mean of the values of the dependent variable. So, here relationship is

T2 = F

this relationship holds because F- test test the variance and t - test is for the standard deviation.

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