Question

PT 15. The data below consists of weights (in pounds) of discarded food and sizes of households. What is the best predicted size of a household that discards 8.00 pounds of food? (Use a 05) Food (x) 1.04 3.68 4.43 2.98 6.30 1.46 8.82 9.62 Size (y) 5ced 0 10 469 443 2920 140 892 Claim (words): 0: H1: Critical value(s): Formula for test value (include inputs): Test value: Decision (reject or fail to reject Ho): Final Wording: Equation of regression line: Best prediction of y when x 8.00:

Answer 1

Claim : To test whether that the discarded food and size of households are correlated or not

Hypothesis : Ho : x and y are not correlated v/s

   H1 : x and y are correlated

Put all the data of x and y in excel worksheet then

by using excel we can calculate the correlation coefficient ( r )

By using command   =CORREL(array1,array2)

we get the correlation coefficient ( r ) = 0.1273

Given that , sample size = n = 8

Test Statistics :    $t = \frac{r * \sqrt{n-2}}{\sqrt{1-r^2}}$

   $t = \frac{0.1272 * \sqrt{8-2}}{\sqrt{1-0.1272^2}}$

$t=0.3141$

$\alpha=0.05$

DF = n - 2 = 8 - 2 = 6

Critical value : tc = 2.447 ..............( From t table)

Decision Rule : We Fail to Reject Ho

Conclusion : There is INSUFFICIENT evidence to conclude that  the discarded food and size of households are correlated.

i.e. x and y are not correlated

i,e, Correlation coefficient is NOT SIGNIFICANT

Therefor , when Correlation coefficient is NOT SIGNIFICANT then $\bar y$ is the BEST PREDICTOR.

$\bar y = \frac{26}{8}=3.25$ .............( ANSWER)

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