Shipping holiday gifts. A December 2010 survey asked 500 randomly sampled Los An

Question

Shipping holiday gifts. 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). (a) Suite the null and alternative hypotheses for testing for independence of age and preferred shipping method for holiday grits among Los Angeles residents. (b) Are the conditions for inference using a chi-square test satisfied?

Explanation / Answer

Answer

(a)

Hypothesis to be tested for testing independence of age and preferred shipping method for holiday gifts among Los Angeles residents is given below.

Null hypothesis: Shipping method for holiday gifts among and age of Los Angeles residents are independent.

Alternative hypothesis: Shipping method for holiday gifts among and age of Los Angeles residents are not independent.

(b)

Conditions for inference using a chi-square test are given below.

·         Sample is drawn by simple random sampling.

·         Sample size (n) should be fairly large.

·         Both variables under study are categorical.

.         All expected frequencies should be a least 5.

Here we can see that sample size is large (n = 500). However expected frequencies of three cells are only 5 and for two cells are less than even 5. Namely for residents with age group 55+ and preferred shipping methods ‘Something else’ and ‘Not sure’ are only 4 and 3 respectively. Hence last condition is not satisfied.

Therefore we can say that, conditions for inference using a chi-square test are not satisfied.

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