In Exercise D.32 we observe that within the random sample of 85 days the city of San Diego has rainy weather just over a quarter of the time. Amy is now curious as to whether there is a rainy season, or if the rainy days are dispersed evenly throughout the year. She separates the 85 days into the four seasons, Spring (Mar€“May), Summer (Jun€“Aug), Fall (Sep€“Nov), and Winter (Dec€“Feb) and observes rainy day counts as seen inTable D.15.

(a) Is the chi-square distribution appropriate for testing this two-way table?
(b) Perform the appropriate test to determine if the proportion of rainy days is different among the four seasons.
(c) State your conclusion(s). If there is a significant difference, when is the rainy season?

Exercise D.32

Amy is interested in moving to California but isn€™t certain which city she€™d prefer. One variable of interest to her is the proportion of rainy days in each city. She took a random sample of days from 2010 for each of the four biggest cities in California (Los Angeles, San Francisco, San Diego, and San Jose) and recorded the results in Table D.14. If a day contained any precipitation it is considered a rainy day.

Table D.14

Spring Summer Winter Fall Rain 5 16 11 11 No Rain 14 Total LA SF SD SJ 6. 17 35 121 3 Rain No Rain 21 22 63 20 Total 25 23 23 156 85 3.