In a certain year, there were 80 days with measurable snowfall in Denver, and 63 days with measurable snowfall in Chicago. A meteorologist computes (80 + 1)/(365 + 2) = 0.22, (63 + 1)/(365 + 2) = 0.17, and proposes to compute a 95% confidence interval for the difference between the proportions of snowy days in the two cities as follows:

Is this a valid confidence interval? Explain.

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0.22 – 0.17 ± 1.961 (0.22)(0.78) (0.17)(0.83) + 367 367