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

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

(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.)

The hypothesis being tested is:

H₀: µ₁ = µ₂

H_a: µ₁ ≠ µ₂

The output is:

p1	p2	p_c
0.2353	0.4375	0.3
80/340	70/160	150/500
80.	70.	150.
340	160	500

	-0.2022	difference
	0.	hypothesized difference
	0.0439	std. error
	-4.60	z
	4.17E-06	p-value (two-tailed)

	-0.2913	confidence interval 95.% lower
	-0.1131	confidence interval 95.% upper
	0.0891	margin of error

Since the p-value is less than the significance level, we can reject the null hypothesis.

Therefore, we can conclude that there is a difference in the proportion of roofs with visible snow accumulation between dark colored roofs and light colored roofs.

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

The 95% confidence interval for the difference in proportion of dark and light roofs with snow accumulation is -0.2913 between and -0.1131.

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

Snow varies from region to region.

milcah answered 2 months ago

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