A Wisconsin resident was curious whether the color of roofing materials had any association with snow...

A Wisconsin resident was curious whether the color of roofing materials had any association with snow accumulation in Wisconsin. One day after a surprising October snowfall, they went to the top of the Capitol Building and examined the 500 visible distinct roofs with a pair of binoculars, and found 340 dark colored roofs and 160 light colored roofs. Of the dark colored roofs, 80 still had visible snow accumulation, while 70 of the light colored roofs still had visible snow.

(a) Perform a hypothesis test at the 5% level of significance to determine if there is evidence of a difference in the proportion of roofs with visible snow accumulation between dark colored roofs and light colored roofs. (Be sure to state your hypotheses and show your computations.)

(b) Create a 95% confidence interval for the difference in proportion of dark and light roofs with snow accumulation.

(c) State one reason why the resident’s observations may not be independent.

Expert Solution

Let denote he proportion of roofs with visible snow accumulation among dark colored roofs and light colored roofs respectively.

a)

b)

orchestra answered 1 year ago

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