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At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are 60%,30%60 \%, 30 \%, and 10%10 \%, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

d) Find the α=0.05\alpha=0.05 critical value for the χ2\chi^2 distribution with the appropriate number of df\mathrm{df}.

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d)

The critical value for the chi-square statistic is determined by the level of significance and the degrees of freedom. And it can be found in the chi-square distribution table.

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