Question

A December 2010 survey asked 500 randomly sampled Los Angeles residents which shipping carrier they prefer to use for shipping holiday gifts. The table below shows the distribution of responses by age group as well as the expected counts for each cell (shown in parentheses).

			Age
	18-34	35-54	55+	Total
Shipping Method
USPS	72 (81)	97 (102)	76 (68)	245
UPS	52 (53)	76 (62)	34 (41)	162
FedEx	31 (21)	24 (27)	9 (16)	64
Something else	7 (5)	6 (7)	3 (4)	16
Not sure	3 (5)	6 (5)	4 (3)	13
Total	165	209	126	500

1. State the null and alternative hypotheses for testing for independence of age and preferred shipping method for holiday gifts among Los Angeles residents.

Null hypothesis: Age and preferred shipping method ?areare not independent.

Alternative hypothesis: Age and preferred shipping method ?areare not independent.

2. Are the conditions for inference using a chi-square test satisfied?

A. Yes, all conditions are satisfied
B. No, too few degrees of freedom
C. No, expected values are too small
D. No, cases are not independent
E. There is not enough information to tell

Answer 1

Answer:

HO; There is no relation between age and preferred shipping method for holiday gifts H1: There is relation between age and preferred shipping method for holiday gifts Observed Frequencies 18-34 35-54 72 52 31 Total 55+ 76 34 USPS UPS FedEx Something else 7 Not sure Total 97 245 76 162 6 6 209 64 16 13 500 4 165 126

The expected Frequencies 35-54 102.41 67.716 26.75 6.69 5.43 208.996 18-34 55+ Total USPS UPS FedEx Something else 5.28 Not sure Total 80.85 61.74 245 40.824 16.13 4.03 53.46 162 21.12 64 16 4.29 3.28 13 165 126.004 500

The chi-square contribution values are 72 52 31 0.9687 0.0399 4.6219 0.5603 0.3879 10241 0.2858 67.716 1.0134 26.75 0.2827 0.0712 0.0598 3.2936 40.824 1.1407 3.1517 0.2633 80.85 53.46 21.12 4.29 76 6.69 5.43 61.74 76 34 16.13 4.03 0.158 Total: 16.2989

Degrees of freedom: 8 Test Statistic, XA2: 16.299 Critical XA2: 15.5073 P-Value: 0.0383 Here P-value < alpha 0.05 so we do not accept Ho Thus we conclude that there is relation between age and preferred shipping method for holiday gifts