Drivers born under the astrological sign of Capricorn are the worst drivers in Australia, according to an article that appeared in the Australian newspaper The Mercury (October 26, 1998). This statement was based on a study of insurance claims that resulted in the following data for male policyholders of a large insurance company

a. Assuming that it is reasonable to treat the male policyholders of this particular insurance company as a random sample of male insured drivers in Australia, are the observed data consistent with the hypothesis that the proportion of male insured drivers is the same for each of the 12 astrological signs?
b. Why do you think that the proportion of Capricorn policyholders is so much higher than would be expected if the proportions are the same for all astrological signs?
c. Suppose that a random sample of 1000 accident claims submitted to this insurance company is selected and each claim classified according to the astrological sign of the driver. (The accompanying table is consistent with accident rates given in the article.)

Test the null hypothesis that the proportion of accident claims submitted by drivers of each astrological sign is consistent with the proportion of policyholders of each sign. Use the given information on the distribution of policyholders to compute expected frequencies and then carry out an appropriate test.

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Number of Astrological Sign Policyholders 35,666 37,926 38,126 54,906 37,179 37,354 37,910 36,677 34,175 35,352 37,179 37,718 Aquariu Aries Cancer Capricorn Gemni Leo Libra sces Sagittarius Scorpio Taurus Virgo Observed Number in Sample 85 83 82 Astrological Sign Aquarius Aries Cancer Capricorn Gemini Leo Libra Pisces 83 83 83 82 81 Sagittarius Observed Number in Sample 85 84 81 Astrological Sign ScorpiO Taurus Virgo