Question

Please label, and answer questions 1-7

Cerámica América makes both commercial and home sinks, toilets, and tile throughout Latin America. There have been many complaints that its commercial sinks are of poor quality. Recently, a new type of home sink, Modelo Americano, has been developed. The company hopes that this new model is of better quality. Quality Control tests sinks using the following three tests:

Cracked or Chipped Ceramic:
Pass (P) or Fail (F)

Glaze Quality:
Pass (P) or Fail (F)

Stress Test
Pass (P) or Fail (F)

A sink gets a “Passing” grade if it passes all three of the above Traditionally, 85% of its commercial sinks have gotten a “Passing” grade. Cerámica América would like to see if its passing rate is better than the traditional rate. Recently, 200 Modelo Americano sinks were randomly chosen from its manufacturing plants. The complete data set is in the file named Sinks.

Managerial Report

Prepare a report (see below) for Cerámica América that summarizes your assessment of its Modelo Americano sinks. Be sure to include the following seven items in your report.

1 To summarize the data, compute the proportion of all sinks that

“Passed” the Cracked or Chipped test.

“Passed” the Glaze Quality test.

“Passed” the Stress Test.

2 Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that got a “Passing” grade. What is the margin of error? What are the lower (or left) and upper (or right) endpoints of the confidence interval? Interpret your results.

3 Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that passed the Cracked or Chipped test. What is the margin of error? What are the lower (or left) and upper (or right) endpoints of the confidence interval? Interpret your results.

4 Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that passed the Glaze Quality test. What is the margin of error? What are the lower (or left) and upper (or right) endpoints of the confidence interval? Interpret your results.

5 Develop the 98% confidence interval for the proportion of all Modelo Americano sinks that passed the Stress Test. What is the margin of error? What are the lower (or left) and upper (or right) endpoints of the confidence interval? Interpret your results.

6 Conduct a hypothesis test (using either the p-Value Approach or the Critical Value Approach) to determine if the proportion of all Modelo Americano sinks that get a “Passing” grade is larger than the than the traditional “Passing” rate. Use α = 0.02. Do not forget to include the correctly worded hypotheses and show all the steps required to conduct the hypothesis test.

7 What advice would you give to Cerámica América based upon your analysis of the data? What is the magnitude of the improvement (if any)? How can this study be improved?

Sink	Cracked or Chipped Test	Glaze Quality Test	Stress Test
1	F	F	F
2	P	P	P
3	P	P	F
4	P	P	P
5	P	P	F
6	P	P	P
7	P	P	P
8	P	F	F
9	F	P	P
10	F	P	F
11	P	P	P
12	P	P	P
13	P	P	P
14	P	P	P
15	P	P	P
16	P	P	P
17	F	P	F
18	F	F	P
19	P	P	P
20	P	P	P
21	P	P	P
22	P	P	P
23	P	P	P
24	P	P	P
25	P	P	P
26	P	P	P
27	P	P	P
28	P	P	P
29	F	P	F
30	P	P	P
31	F	P	P
32	P	P	P
33	P	P	P
34	P	P	P
35	P	P	P
36	P	P	P
37	P	P	P
38	F	F	F
39	P	P	P
40	F	F	F
41	P	P	P
42	P	P	P
43	P	P	P
44	P	P	P
45	P	P	P
46	P	P	P
47	P	P	P
48	P	P	P
49	P	P	P
50	P	P	P
51	P	P	P
52	P	P	P
53	P	P	P
54	P	P	P
55	P	P	P
56	F	F	F
57	P	P	P
58	P	P	P
59	P	P	P
60	P	P	P
61	P	P	P
62	P	P	P
63	P	P	P
64	P	P	P
65	P	P	P
66	P	P	P
67	P	P	P
68	P	P	P
69	P	P	P
70	P	P	P
71	P	P	P
72	P	P	P
73	P	P	P
74	P	P	P
75	P	P	P
76	P	P	P
77	P	P	P
78	P	P	P
79	P	P	P
80	P	P	P
81	P	P	P
82	P	P	P
83	P	P	P
84	P	P	P
85	P	P	P
86	F	F	F
87	P	P	P
88	P	P	P
89	P	P	P
90	P	P	P
91	P	P	P
92	P	P	P
93	P	P	P
94	P	P	P
95	P	P	P
96	P	P	P
97	P	P	P
98	P	P	P
99	P	P	P
100	P	P	P
101	P	P	P
102	P	P	P
103	P	P	P
104	P	P	P
105	P	P	P
106	P	P	P
107	F	P	P
108	F	P	P
109	P	P	P
110	F	F	F
111	F	F	F
112	P	P	P
113	P	P	P
114	P	P	P
115	P	P	P
116	P	P	P
117	P	P	P
118	P	P	P
119	P	P	P
120	P	P	P
121	P	P	P
122	P	P	P
123	P	P	P
124	P	P	P
125	P	P	P
126	P	P	P
127	P	P	P
128	P	P	P
129	P	P	P
130	P	P	P
131	P	P	P
132	P	P	P
133	P	P	P
134	P	P	P
135	P	P	P
136	P	P	P
137	P	P	P
138	P	P	P
139	P	P	P
140	P	P	P
141	P	P	P
142	P	P	P
143	P	P	P
144	P	P	P
145	P	P	P
146	P	P	P
147	P	P	P
148	P	P	P
149	P	P	P
150	P	P	P
151	P	P	P
152	P	P	P
153	P	P	P
154	P	P	P
155	P	P	P
156	P	P	P
157	P	P	P
158	F	F	F
159	P	P	P
160	P	P	P
161	P	P	P
162	P	P	P
163	P	P	P
164	P	P	P
165	P	P	P
166	P	P	P
167	P	P	P
168	P	P	P
169	P	P	P
170	P	P	P
171	P	P	P
172	P	P	P
173	P	P	P
174	P	P	P
175	P	P	P
176	P	P	P
177	P	P	P
178	P	P	P
179	P	P	P
180	P	P	P
181	P	P	F
182	P	P	P
183	P	P	P
184	P	P	P
185	P	P	P
186	P	P	P
187	P	P	P
188	P	P	P
189	P	P	P
190	P	P	P
191	P	P	P
192	P	P	P
193	P	P	P
194	P	P	P
195	P	P	P
196	P	P	P
197	P	P	P
198	P	P	P
199	P	P	P
200	P	P	P

Answer 1

Frequency	Cracked or chipped test	Glazer Quality Test	Stress Test	Overall Pass
Passed	184	190	185	180
Failed	16	10	15	20
Pass Proportion()	184/200=0.92	190/200=0.95	185/200=0.925	180/200=0.9

Confidence interval for proportion is given by the formula

Here z is the value from the standard normal table for the confidence level 98% use

https://surfstat.anu.edu.au/surfstat-home/tables/normal.php. The screenshot for the calculation is provided below

z=2.326

Substitute the value in the above interval. I will calculate the interval for one variable Overall Pass

Confidence interval =

Margin of error =

In the same manner try constructing confidence interval and margin of error for other variables

98% Confidence interval can be interpreted as the interval within which 98% of the sample proportions lie

6) To test H₀: p=0.85 (p₀) vs H₁: p>0.85

The test statistic to test H₀ is

Now the criteria to reject H₀ for this one tailed test is

reject H₀ if z> z_0.02( value obtained from standard normal table)

z_0.02 =2.326. Its eviddent that z<z_0.02 so rejection nof H₀ is not possible...Passing rate has not been improved