A local news 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).

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

(b) Are the conditions for inference using a chi-square test satisfied?

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