For(b) A more detailed theory predicts that the 4 types of tomato plant given above appear in a

9:3:3:1 (tall cut : tall potato : dwarf cut : dwarf potato) ratio. Perform a chi-square goodness

of fit test to check whether the data support this theory or not.

i. List Ho and Ha.

Ho: p1= 0.5625, p2= 0.1875, p3= 0.1875 and p4= 0.0625

H1: not all p1 are as specified in Ho

ii. Find the expected value under Ho for each observation in the table.

E(11) = 0.5625 x 1611 = 906.19

E(12) = 0.1875 x 1611 = 302.06

E(21) = 0.1875 x 1611 = 302.06

E(22) = 0.0625 x 1611 = 100.69

iii. Calculate the chi-square test statistic and specify its degrees of freedom.

Chi-Sq = (((926-906.19)^2)/906.19) + (((288-302.06)^2)/302.06) + (((293-302.06)^2)/302.06) + (((104-100.69)^2)/100.69)

= 0.433 + 0.654 + 0.272 + 0.11

= 1.469

d.f. = 4-1

= 3