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.

Astrological Sign Number of Policyholders Aquarius 35,666 Aries 37,926 Cancer 38,126 Capricorn 54,906 Gemini 37,179 Leo 37,354 Libra 37,910 Pisces 36,677 Sagittarius 34,175 Scorpio 35,352 Taurus 37,179 Virgo 37,718

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.)
Astrological Sign Observed Number in Sample Aquarius 85 Aries 83 Cancer 82 Capricorn 88 Gemini 83 Leo 83 Libra 83 Pisces 82 Sagittarius 81 Astrological Sign Observed Number in Sample Scorpio 85 Taurus 84 Virgo 81 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.