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 3 months ago

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....

Roofing Manufacturers had a beginning work-in-progress of $500,000. The company used $300,000 in direct materials and...

Roofing Manufacturers had a beginning work-in-progress of $500,000. The company used $300,000 in direct materials and $500,000 in labor and applied factory overhead at 200% of direct materials. At the end of the month, the company had an ending work-in-progress of $750,000. Record necessary journal entries to record the (1) direct materials used, (2) direct labor used, (3) applied overhead and (4) the transfer of completed work-in-progress from molding department to finishing department. (20 Points)

You are a financial advisor and your clients are curious whether the Trump administration has had...

You are a financial advisor and your clients are curious whether the Trump administration has had a positive impact on the stock market. In order to test the hypothesis; you select 15 Blue chip stocks. The following is the price of the stock 1 week before the election and 1 week after… BBY 45.23 50.11 GM 101.22 105.22 TGT 67.09 73.11 AAPL 156.88 162.44 MAT 25.99 24.88 F 69.02 78.11 C 69.98 74.00 GOOG 308.11 332.06 PETM 34.99 35.11 BCS 101.88 103.22 BSX 78.22 74.20 ADP 56.11 57.90 IBM 134.09 150.68 T 89.44 93.12 YHOO 45.98 46.11 What type of statistical analysis would you conduct and why? What is your...

The director of an alumni association wants to determine whether there is any type of relationship...

The director of an alumni association wants to determine whether there is any type of relationship between the amount of an alumni's contribution (in dollars) and the number of years the alumnus has been out of school. Based on the data below, compute the value of the correlation coefficient between the number of years and the amount of the contribution. Years x 1 3 4 10 9 7 Contribution y 630 180 210 30 90 90

Q5. [20] We would like to determine whether any association exists between the survival time and...

Q5. [20] We would like to determine whether any association exists between the survival time and level of water toxicity, region and age of the patients. Survival time is coded as 1 if < 1 month, 2 = 1-3 months, and 3 = more than 3 months. Survival Region Toxic Level Age 1 1 62.00 67 1 2 46.00 72 2 1 48.50 56 3 2 32.00 35 2 1 63.50 60 1 1 41.25 65 2 2 40.00 45...

When assessing a credit application, it must be determined whether the customer previously had any loans...

When assessing a credit application, it must be determined whether the customer previously had any loans or accounts with the same bank at which the customer now applies for a loan, and to assess how well such accounts were managed by their customer. Select one of the listed items below that will be the best source of information for this purpose. (Please note: only ONE of the options is correct). a. Trade references. b. Bank statements. c. Credit bureau report....

A researcher would like to determine whether a new tax on cigarettes has had any effect...

A researcher would like to determine whether a new tax on cigarettes has had any effect on people’s behavior. During the year before the tax was imposed, stores located in rest areas on the state thruway reported selling an average of µ = 410 packs per day with σ = 60. The distribution of daily sales was approximately normal. For a sample of n = 9 days following the new tax, the researcher found an average of M = 386...

1. It's unclear whether Genie had any mental retardation (either from birth or as a result...

1. It's unclear whether Genie had any mental retardation (either from birth or as a result of her abuse). Why does this fact make her case problematic for deriving clear conclusions about the Critical Period Hypothesis? 2. Does Genie's learning of vocabulary words constitute acquisition of language? Why or why not? If it is language, then why should she have been able to learn some vocabulary, but not able to learn rules of grammar (i.e., syntax and morphology)? 3. Can...

Seller agreed to sell to Buyer a quantity of raw materials. The written contract provided that notice of defects, to be effective, had to be received by Seller before any use or within ten days of receipt

Seller agreed to sell to Buyer a quantity of raw materials. The written contract provided that notice of defects, to be effective, had to be received by Seller before any use or within ten days of receipt. When the raw materials were processed by Buyer, they turned a rust color, producing a finished product that was difficult to sell to ultimate customers. Buyer immediately notified Seller of the problem and refused to pay, claiming that the defect made the finished...

Question