A company would like to estimate its total cost equation. It has collected 48 months of monthly production output and corresponding total production costs.  The collected data is in the file Production Cost Data Only.xlsx. Recall that

TOTAL COST = Fixed Costs + Variable Cost per Unit *Output.

Use the data to estimate a function that describes total cost for this company. (Round answers to 2 decimal places)

Develop a scatterplot of the two variables: monthly output and monthly total costs. Describe the relationship.

Estimate a total cost curve for this company.  State the estimated total cost function.

Based on your estimated total cost curve what is the estimated Fixed Cost for the Company?

Based on your estimated total cost curve what is the estimated average unit variable cost for the Company?

Develop a 95% confidence interval for the true average variable cost per unit.

What percent of the variation in monthly production costs is “explained” by the monthly production output?

Suppose the plant manager is interested in mean costs for several monthswhere output averages 30,000 units (i.e., Xp = 30). What is the predicted monthly total costs when output averages 30?  Construct a 95% confidence interval for the mean production costs for months that average 30,000 units of output.

Monthly Output (in thousands of units)	Monthly Total Production Cost (in thousand $)
47	926
45	888
42	841
43	888
42	863
42	898
41	885
48	911
41	812
40	837
39	845
39	856
40	858
38	852
39	877
39	926
37	915
37	841
37	812
37	833
36	822
38	809
37	769
38	783
41	745
38	716
39	656
39	620
37	616
35	771
34	754
34	703
32	667
31	643
28	540
25	502
20	436
17	380
14	314
13	294
10	290
10	190
9	203
8	176
8	192
6	149
5	114
4	126

We are to distribute 10 colored balls into five containers. Do the following:

1. Compute the probability of having at least one ball in each bucket if the balls are all different and the buckets are all labeled differently.

2. Compute the probability of having at least one ball in each bucket if the balls are all different and the buckets are all gray.

3. Compute the probability of having at least one ball in each bucket if the balls are gray and the buckets are all labeled differently.

4. Which one gives the most likelihood?

You are curious about the role of graduate status on work-life balance in Tech students. In a sample of 100 undergraduate students, 37 reported having trouble balancing school and work. In a separate sample of 75 graduate students, 50 had trouble with this balance. Test the null hypothesis that undergraduate or graduate students are equally likely to have trouble with work-life balance (alpha=0.05).

For independent sample t-tests: mean values for each sample, the variances for each sample, estimated standard error of the difference in means, the t-ratio, degrees of freedom, the t-critical value, and your decision to reject or retain the null.

For dependent sample t-tests: mean values for each sample, standard deviation for the difference between groups, standard error of the difference between the means, the t-ratio, degrees of freedom, the t-critical value, and your decision to reject or retain the null.

For proportions: sample proportions, combined proportions, standard error of the difference, z-score, critical z-score, and your decision to reject or retain the null.

Thirty small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 45.1 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit:

upper limit:

margin of error:

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit:

upper limit:

margin of error:

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit:

upper limit:

margin of error:

(d) Compare the margins of error for parts (a) through (c). As the confidence levels increase, do the margins of error increase?

As the confidence level increases, the margin of error increases.

As the confidence level increases, the margin of error remains the same.

As the confidence level increases, the margin of error decreases.

(e) Compare the lengths of the confidence intervals for parts (a) through (c). As the confidence levels increase, do the confidence intervals increase in length?

As the confidence level increases, the confidence interval decreases in length.

As the confidence level increases, the confidence interval remains the same length.

As the confidence level increases, the confidence interval increases in length.

Consider the Nomad Machine Company (NMC) problem from class. As the problem stated: "you should develop two flow models" because NMC has sought "to build a new factory to expand its production capacity". Your task was to determine which factory to recommend.

In this discussion assignment, upload the JPG outcome for the optimal solution. Your uploaded solution should have a similar 'look and feel' professionalism as the JPG file on the external site (figure TP-F8). Make sure to use solver so the pink cells are populated. Also, using this optimal site selection, provide the operating costs for Cincinnati, Kansas City, and Pittsburgh.

A student group believes that less than 50% of students find their college experience extremely rewarding. They decide to test this hypothesis using a significance level of .05. They conduct a random sample of 100 students and 34 say they find their college experience extremely rewarding.

Based on the type of test this is (right, left, or two-tailed); determine the following for this problem.

4. Critical Value(s): _______________________

5. P-value Table A.3 _______________________ P-value Calculator:________________

P-value Table A.2 _______________

6: Can you reject? _______________________

7. Conclusion: Can we conclude or can we not conclude less than 50% of students find their college experience extremely rewarding? (write the conclusion in a sentence)

A survey found that​ women's heights are normally distributed with mean 62.3 in. and standard deviation 3.6 in. The survey also found that​ men's heights are normally distributed with mean 67.7 in. and standard deviation 3.3 in. Consider an executive jet that seats six with a doorway height of 55.7 in. Complete parts​ (a) through​ (c) below.

a. What percentage of adult men can fit through the door without​ bending?

The percentage of men who can fit without bending is

___.

​(Round to two decimal places as​ needed.)

b. Does the door design with a height of

55.755.7

in. appear to be​ adequate? Why​ didn't the engineers design a larger​ door?

A.

The door design is​ inadequate, but because the jet is relatively small and seats only six​ people, a much higher door would require major changes in the design and cost of the​ jet, making a larger height not practical.

B.

The door design is​ adequate, because the majority of people will be able to fit without bending.​ Thus, a larger door is not needed.

C.

The door design is​ adequate, because although many men will not be able to fit without​ bending, most women will be able to fit without bending.​ Thus, a larger door is not needed.

D.

The door design is​ inadequate, because every person needs to be able to get into the aircraft without bending. There is no reason why this should not be implemented.

c. What doorway height would allow​ 40% of men to fit without​ bending?

The doorway height that would allow​ 40% of men to fit without bending is

__

in.

​(Round to one decimal place as​ needed.)

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6950 and estimated standard deviation σ = 2650. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. (a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.) (b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? The probability distribution of x is not normal. The probability distribution of x is approximately normal with μx = 6950 and σx = 1873.83. The probability distribution of x is approximately normal with μx = 6950 and σx = 1325.00. The probability distribution of x is approximately normal with μx = 6950 and σx = 2650. What is the probability of x < 3500? (Round your answer to four decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) (d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased? The probabilities decreased as n increased. The probabilities stayed the same as n increased. The probabilities increased as n increased. If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse? It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia. It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia. It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia. It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

The mass of plants in a botany lab are normally distributed with a mean of 54 grams and a standard deviation of 6.5 grams. Use this to compute : a. The probability that one randomly chosen plant will have a mass that less than 49.25 grams b. The probability that one randomly chosen plant will have a mass that is between 52 grams and 62 grams. c. The mass of a plant which weighs less than the top 15% of plants in the lab. d. The probability that 25 randomly chosen plants will have a mean mass of no more than 50 grams

What is the critical F value when the sample size for the numerator is sixteen and the sample size for the denominator is ten? Use a two-tailed test and the 0.02 significance level. (Round your answer to 2 decimal places.)

An evaluation was recently performed on brands and data were collected that classified each brand as being in the technology or financial institutions sector and also reported the brand value. The results in terms of value​ (in millions of​ dollars) are shown in the accompanying data table. Complete parts​ (a) through​ (c).

BRAND VALUES:

Technology: 281, 377, 491, 429, 406, 584, 641, 624

Financial Institutions: 517, 832, 819, 804, 937, 995, 1035, 1094

a.)

Assuming the population variances are​ equal, is there evidence that the mean brand value is different for the technology sector than for the financial institutions​ sector? (Use α=0.05​.)

Determine the hypotheses. Let μ1 be the mean brand value for the technology sector and μ2 be the mean brand value for the financial institutions sector. Choose the correct answer below.

A.) H0: μ1= μ2

H1: μ1≠μ2

B.) H0: μ1≤ μ2

H1: μ1 > μ2

C.) H0: μ1≥ μ2

H1: μ1< μ2

D.) H0: μ1≠μ2

H1: μ1=μ2

-Find the test statistic.

^tSTAT=___

-Choose the correct answer below.

A. Reject H0. There is sufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

B. Reject H0. There is insufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

C. Do not reject H0. There is sufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

D.Do not reject H0. There is insufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

b.)

-Repeat​ (a), assuming that the population variances are not equal.

A.) H0: μ1= μ2

H1: μ1≠μ2

B.) H0: μ1≤ μ2

H1: μ1 > μ2

C.) H0: μ1≥ μ2

H1: μ1< μ2

D.) H0: μ1≠μ2

H1: μ1=μ2

-FInd the test statistic.

^tSTAT=____

-Choose the correct answer below.

A. Reject H0. There is sufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

B. Reject H0. There is insufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

C. Do not reject H0. There is sufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

D.Do not reject H0. There is insufficient evidence that the mean brand value for the technology sector is different from the mean brand value for the financial institutions sector.

c.)

-Compare the results of (a) and (b).

A. The conclusions for parts​ (a) and​ (b) are different. Reject the null hypothesis in​ (b) and do not reject it in​ (a).

B.The conclusions for parts​ (a) and​ (b) both reject the null hypothesis.

C.The conclusions for parts​ (a) and​ (b) both do not reject the null hypothesis.

D. The conclusions for parts​ (a) and​ (b) are different. Reject the null hypothesis in​ (a) and do not reject it in​ (b).

The following counts of vehicles arriving at a toll station, over 1-minute intervals, were made by an engineering student: 2,0,4,1,2,4,2,1,6,2,5,4,4,3,3,2,2,1,2,3,2,5,2,0,1,2,0,3,1,1, 2,3,5,6,3,4,3,4,0,6,3,2,1,4,4,0,1,4,3,7,0,0,2,3,2,4,3,2,4,5 (a) Assuming the vehicle arrivals were generated by a Poisson process, compute the maximum likelihood estimate of the arrival rate. (b) Test the hypothesis that the arrival counts follow a Poisson distribution, at the α=0.05 significance level.

Drive-through Service Time at McDonald’s When you are on the go and looking for a quick meal, where do you go? If you are like millions of people every day, you make a stop at McDonald’s. Known as “quick service restaurants” in the industry (not “fast food”), companies such as McDonald’s invest heavily to determine the most efficient and effective ways to provide fast, high quality service in all phases of their business. Drive-through operations play a vital role. It’s not surprising that attention is focused on the drive-through process. After all, over 60% of the individual restaurant revenues in the United States come from the drive-through operations. Yet understanding the process is more complex than just counting cars. Marla King, professor at the company’s international training center, Hamburger University, got her start 25 years ago working at a McDonald’s drive-through. She now coaches new restaurant owners and managers. “Our stated drive-through service time is 90 seconds or less. We train every manager and team member to understand that a quality customer experience at the drive-through depends on them,” says Marla. Some of the factors that affect a customers’ ability to complete their purchases with 90 seconds include restaurant staffing, equipment layout in the restaurant, training, and efficiency of the grill team, and frequency of customer arrivals to name a few. Customer order patterns also play a role. Some customers will just order drinks, while others seem to need enough food to feed an entire soccer team. And then there are the special orders. Obviously, there is plenty of room for variability here. Yet that doesn’t stop the company from using statistical techniques to better understand the drive-through action. In particular, McDonald’s utilizes numerical measures of the center (mean) and spread (variance) in the data and to help transform the data into useful information. In order for restaurant managers to achieve the goal in their own restaurants, they need training in proper restaurant and drive-through operations. Hamburger University, McDonald’s training center located near Chicago, Illinois, satisfies that need. In the mock-up restaurant service lab, managers go through a “before and after” training scenario. In the “before” scenario, they run the restaurant for thirty minutes as if they were back in their home restaurants. Managers in the training class are assigned to be crew, customers, drive-through cars, special needs guests (such as hearing impaired), or observers. Statistical data about the operations, revenues, and service times are collected and analyzed. Without the right training, the restaurant’s operation usually starts breaking down after 10-15 minutes. After debriefing and analyzing the data collected, the managers make suggestions for adjustments and head back to the service lab to try again. This time, the results usually come in well within standards. “When presented with the quantitative results, managers are pretty quick to make the connections between better operations, higher revenues, and happier customers,” Marla states. When managers return to their respective restaurants, the training results and techniques are shared with staff who are charged with implementing the ideas locally. The results of the training eventually are measured when McDonald’s conducts a restaurant operations improvement process study, or ROIP. The goal is simple: improved operations. When the ROIP review is completed, statistical analyses are performed and managers are given their results. Depending on the results, decisions might be made that require additional financial resources, building construction, staff training, or reconfiguring layouts. Yet one thing is clear: Statistics drive the decisions behind McDonald’s drive-through service operations.

Customer	Customer waiting time (seconds)	Time of Day (1 = Breakfast, 2 = Lunch, 3 = Dinner)
1	85	1
2	74	1
3	64	1
4	90	1
5	93	1
6	102	1
7	72	1
8	96	1
9	79	1
10	91	1
11	89	1
12	75	1
13	75	1
14	96	1
15	82	1
16	87	1
17	76	1
18	92	1
19	81	1
20	76	1
21	64	1
22	94	1
23	87	1
24	82	1
25	101	1
26	82	1
27	76	1
28	73	1
29	56	1
30	73	1
31	84	1
32	69	1
33	102	1
34	74	1
35	75	1
36	78	1
37	93	1
38	81	1
39	82	1
40	86	1
41	72	1
42	89	1
43	91	1
44	95	1
45	86	1
46	98	1
47	108	1
48	77	1
49	78	1
50	96	1
51	87	1
52	87	1
53	91	1
54	99	1
55	65	1
56	109	1
57	87	1
58	101	1
59	73	1
60	94	1
61	82	1
62	79	1
63	89	1
64	105	1
65	92	1
66	78	1
67	101	1
68	86	1
69	105	1
70	86	1
71	89	1
72	76	1
73	81	1
74	99	1
75	95	1
76	77	1
77	90	1
78	74	1
79	360	1
80	96	1
81	98	1
82	75	1
83	83	1
84	98	1
85	87	1
86	95	1
87	73	1
88	83	1
89	105	1
90	83	1
91	68	1
92	94	1
93	107	1
94	84	1
95	93	1
96	75	1
97	73	1
98	86	1
99	100	1
100	96	1
101	91	1
102	68	1
103	90	1
104	85	1
105	77	1
106	72	1
107	87	1
108	87	1
109	96	1
110	76	1
111	67	1
112	94	1
113	76	1
114	78	1
115	85	1
116	93	1
117	79	1
118	82	1
119	66	1
120	86	1
121	96	2
122	84	2
123	68	2
124	60	2
125	92	2
126	85	2
127	80	2
128	92	2
129	86	2
130	98	2
131	77	2
132	83	2
133	85	2
134	110	2
135	85	2
136	79	2
137	87	2
138	87	2
139	78	2
140	102	2
141	85	2
142	75	2
143	64	2
144	97	2
145	84	2
146	116	2
147	105	2
148	84	2
149	77	2
150	85	2
151	86	2
152	85	2
153	68	2
154	108	2
155	73	2
156	90	2
157	91	2
158	102	2
159	95	2
160	71	2
161	143	2
162	70	2
163	98	2
164	102	2
165	66	2
166	99	2
167	103	2
168	76	2
169	72	2
170	93	2
171	78	2
172	85	2
173	76	2
174	105	2
175	99	2
176	92	2
177	87	2
178	68	2
179	87	2
180	93	2
181	75	2
182	70	2
183	103	2
184	73	2
185	78	2
186	62	2
187	82	2
188	74	2
189	83	2
190	98	2
191	98	2
192	106	2
193	77	2
194	92	2
195	82	2
196	82	2
197	78	2
198	93	2
199	88	2
200	112	2
201	85	2
202	103	2
203	76	2
204	91	2
205	73	2
206	77	2
207	73	2
208	72	2
209	95	2
210	59	2
211	98	2
212	81	2
213	102	2
214	73	2
215	83	2
216	99	2
217	88	2
218	101	2
219	109	2
220	102	2
221	70	2
222	62	2
223	84	2
224	79	2
225	94	2
226	78	3
227	98	3
228	78	3
229	85	3
230	108	3
231	67	3
232	95	3
233	106	3
234	78	3
235	83	3
236	61	3
237	90	3
238	72	3
239	72	3
240	80	3
241	90	3
242	82	3
243	75	3
244	72	3
245	94	3
246	65	3
247	88	3
248	68	3
249	114	3
250	110	3
251	101	3
252	81	3
253	83	3
254	102	3
255	85	3
256	87	3
257	75	3
258	71	3
259	94	3
260	87	3
261	92	3
262	90	3
263	91	3
264	79	3
265	81	3
266	65	3
267	89	3
268	72	3
269	86	3
270	144	3
271	58	3
272	92	3
273	76	3
274	79	3
275	97	3
276	61	3
277	73	3
278	98	3
279	111	3
280	81	3
281	88	3
282	71	3
283	82	3
284	72	3
285	67	3
286	105	3
287	98	3
288	87	3
289	70	3
290	76	3
291	107	3
292	300	3
293	95	3
294	66	3
295	95	3
296	82	3
297	85	3
298	86	3
299	106	3
300	93	3
301	102	3
302	80	3
303	84	3
304	101	3
305	82	3
306	78	3
307	103	3
308	102	3
309	85	3
310	98	3
311	100	3
312	71	3
313	98	3
314	100	3
315	98	3
316	99	3
317	93	3
318	107	3
319	75	3
320	77	3
321	75	3
322	100	3
323	91	3

Questions:

1. After returning from the training session at Hamburger University, a McDonald’s store owner
selected a random sample of 323 drive-through customers and carefully measured the time it took
from when a customer entered the McDonald’s property until the customer had received the order at
the drive-through window.
These data are provided, using Excel spreadsheet. Note that the owner
selected some customers during the breakfast period, others during lunch or dinner time. For the
overall sample, compute the key measures of the central tendency and variation.
Based on these measures, what conclusion might the owner reach with respect to how well his store is
doing in meeting the 90 second customer service goal? Support your argument with appropriate
hypothesis testing.

2. Compute the key measures of central tendency and variation for drive-through times broken down by
breakfast, lunch, and dinner time periods. Based on these calculations, does it appear that the store is
doing better at one of these time periods than the others in providing shorter drive-through waiting
times? Support your argument with appropriate hypothesis testing.

3. Determine if there are any outliers in the sample data. Discuss.

show the steps of doing it in excel when answering it please

Share a link to a news article or study that you think exhibits a sampling error or bias. Briefly describe what you think the issue is and how you might fix it.

The factory building manager at Delectable Delights, Jason Short, is concerned that the new contractor he hired is taking too long to replace defective lights in the factory workspace. He would like to perform a hypothesis test to determine if the replacement time for the lights under the new contractor is in fact longer than the replacement time under the previous contractor, which was 3.2 days on average. He selects a random sample of 12 service calls to replace defective lights and obtains the following times to replacement (in days). Use a significance level of 0.05.

6.2       7.1       5.4       5.5       7.5       2.6       4.3       2.9       3.7       0.7       5.6       1.7

Define μ in the context of the problem and state the appropriate hypotheses. (5 pts)

Regardless of your results in Part B, calculate the appropriate test statistic by hand. Write out all your steps. (5 pts)

1. What is your decision regarding the null hypothesis? (In other words, do you reject or fail to reject and why?) (5 pts)
   1. 
      

Write a final concluding statement to Jason giving the results of the hypothesis test. (In other words, write the final summary statement.) (5 pts)