Question

19.12 In Chapter 1, Table 1.1 lists the weights of 53 male statistics students. Although students were asked to report their weights to the nearest pound, inspection of Table 1.1 reveals that a disproportionately large number (27) reported weights end- ing in either a 0 or a 5. This suggests that many students probably reported their weights rounded to the nearest 5 or 10 pounds rather than to the nearest pound. Using the .05 level of significance, test the null hypothesis that in the underlying population, weights are rounded to the nearest pound. (Hint: If the null hypothesis is true, only two-tenths of all weights should end in either a 0 or a 5, and the remain- ing eight-tenths of all weights should end in a 1, 2, 3, 4, 6, 7, 8, or 9. Therefore, the situation requires a one-variable test with only two categories, and df = 1.) foronan (Ruddhist lewish

Answer 1

Reported weights ending in either a 0 or a 5 is 27

Reported weights ending in 1, 2, 3, 4, 6, 7, 8, or 9 is 26

Let P: proportion of all weights should end in either a 0 or a 5

Ho: P=0.2

Ho: P?0.2

Observed (1)	Expected (2)	O - E            (3) = (1) - (2)	(O - E)² / E (4)= (3)2 / (2)
27	10.6	16.4	25.374
26	42.4	-16.4	6.343
53	53	0	31.717
chi-square = 31.717
df                    = 1
p-value        = 0

Critical chi square with df=1 is 3.841

chi square 31.717 which is > 3.841. Ho is rejected

weights are rounded to the nearest pound end in either a 0 or a 5