Question

To generalize to the weights of all male statistics students or all male college students. Table 1.1 QUANTITATIVE DATA: WEIGHTS (IN POUNDS) OF MALE STATISTICS STUDENTS 160 168 133 170 150 165 158 165 193 169 245 160 152 190 179 157 226 160 170 180 150 156 190 156 157 163 152 158 225 135 165 135 180 172 160 170 145 185 152 205 151 220 166 152 159 156 165 157 190 206 172 175 154

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 ending 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 remaining 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.)

Answer 1

Result:

To generalize to the weights of all male statistics students or all male college students. Table 1.1 QUANTITATIVE DATA: WEIGHTS (IN POUNDS) OF MALE STATISTICS STUDENTS 160 168 133 170 150 165 158 165 193 169 245 160 152 190 179 157 226 160 170 180 150 156 190 156 157 163 152 158 225 135 165 135 180 172 160 170 145 185 152 205 151 220 166 152 159 156 165 157 190 206 172 175 154

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 ending 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 remaining 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.)

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

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
	27	10.600	16.400	25.374
	26	42.400	-16.400	6.343
Total	53	53.000	0.000	31.717
	31.717	chi-square
	1	df
	0.0000	p-value

Critical chi square with df=1 is 3.841

Calculated chi square 31.717 which is > 3.841. Ho is rejected.

We conclude that weights are rounded to the nearest pound end in either a 0 or a 5.