#2. The operations manager of a musical instrument distributor feels that demand for a particular type of guitar may be related to the number of YouTube views for a popular music video by the popular rock group Marble Pumpkins during the preceding month. The manager has collected the data shown in the following table: YouTube Views (1000s) Guitar Sales 30 8 40 11 70 12 60 10 80 15 50 13
a. Graph the data to see whether a linear equation might describe the relationship between the views on YouTube and guitar sales.
b. Using the equations presented in this chapter, compute the SST, SSE, and SSR. Find the least squares regression line for the data.
c. Using the regression equation, predict guitar sales if there were 40,000 views last month.
In: Math
1) A door-to-door salesman expects to make a sale 26% of the time when starting the day. But making a sale increases his enthusiasm so much that the probability of a sale to the next customer is 0.36. If he makes no sale, the probability for a sale to the next customer stays at 0.26. What is the probability that he will make at least two sales with his first three visits?
2)Two machines turn out all the products in a factory, with the first machine producing 50% of the product and the second 50%. The first machine produces defective products 2% of the time and the second machine 7% of the time.
(a) What is the probability that a defective part is produced at
this factory given that it was made on the first machine?
(b) What is the probability that a defective part is produced at
this factory?
3)Dystopia county has three bridges. In the next year, the Elder bridge has a 11% chance of collapse, the Younger bridge has a 2% chance of collapse, and the Ancient bridge has a 22% chance of collapse. What is the probability that exactly one of these bridges will collapse in the next year? (Round your final answer to four decimal places. Do not round intermediate calculations.)
In: Statistics and Probability
Individuals who consume large amounts of alcohol do not use the calories from this source as efficiently as calories from other sources. One study examined the effects of moderate alcohol consumption on body composition and the intake of other foods. Fifteen subjects participated in a crossover design where they either drank wine for the first 6 weeks and then abstained for the next 6 weeks or vice versa. During the period when they drank wine, the subjects, on average, lost 0.31 kilograms (kg) of body weight; when they did not drink wine, they lost an average of 1.13 kg. The standard deviation of the difference between the weight lost under these two conditions is 8.4 kg. During the wine period, they consumed an average of 2572 calories; with no wine, the mean consumption was 2557. The standard deviation of the difference was 206.
(a) Compute the differences in means and the standard errors for comparing body weight and caloric intake under the two experimental conditions. (To find the differences, subtract the relevant scores when the participants did not drink wine from the relevant scores when they did drink wine. Round your standard errors to three decimal places.)
| xD | SE | |
| weight | ||
| caloric intake |
(b) A report of the study indicated that there were no significant
differences in these two outcome measures. Verify this result for
each measure, giving the test statistic, degrees of freedom, and
the P-value. (Use
α = 0.10.
Round your answers for t to three decimal places, and round your P-values to four decimal places.)
| df | t | P-value | |
| weight | |||
| caloric intake |
State your conclusion for body weight.
a) Reject the null hypothesis. There is significant evidence of a difference in body weight.
b) Fail to reject the null hypothesis. There is not significant evidence of a difference in body weight.
c) Reject the null hypothesis. There is not significant evidence of a difference in body weight.
d) Fail to reject the null hypothesis. There is significant evidence of a difference in body weight.
State your conclusion for caloric intake.
a) Fail to reject the null hypothesis. There is not significant evidence of a difference in caloric intake.
b)Reject the null hypothesis. There is significant evidence of a difference in caloric intake.
c) Reject the null hypothesis. There is not significant evidence of a difference in caloric intake.
d) Fail to reject the null hypothesis. There is significant evidence of a difference in caloric intake.
(c) One concern with studies such as this, with a small number of
subjects, is that there may not be sufficient power to detect
differences that are potentially important. Address this question
by computing 95% confidence intervals for the two measures and
discuss the information provided by the intervals. (Round your
answers to three decimal places.)
weight ( kg, kg)
caloric intake ( calories, calories)
Discussion:
(d) Here are some other characteristics of the study. The study
periods lasted for 6 weeks. All subjects were males between the
ages of 21 and 50 years who weighed between 68 and 91 kg. They were
all from the same city. During the wine period, subjects were told
to consume two 135-milliliter (ml) servings of red wine per day and
no other alcohol. The entire 6-week supply was given to each
subject at the beginning of the period. During the other period,
subjects were instructed to refrain from any use of alcohol. All
subjects reported that they complied with these instructions except
for three subjects, who said that they drank no more than three to
four 12-ounce bottles of beer during the no-alcohol period. Discuss
how these factors could influence the interpretation of the
results.
In: Statistics and Probability
Problem 6-27 Sales Mix; Break-Even Analysis; Margin of Safety [LO6-7, LO6-9]
Island Novelties, Inc., of Palau makes two products—Hawaiian Fantasy and Tahitian Joy. Each product’s selling price, variable expense per unit, and annual sales volume are as follows:
| Hawaiian Fantasy | Tahitian Joy | |||||
| Selling price per unit | $ | 20 | $ | 100 | ||
| Variable expense per unit | $ | 13 | $ | 40 | ||
| Number of units sold annually | 22,000 | 6,600 | ||||
Fixed expenses total $506,000 per year.
Required:
1. Assuming the sales mix given above, do the following:
a. Prepare a contribution format income statement showing both dollar and percent columns for each product and for the company as a whole.
b. Compute the company's break-even point in dollar sales. Also, compute its margin of safety in dollars and its margin of safety percentage.
2. The company has developed a new product called Samoan Delight that sells for $55 each and that has variable expenses of $44 per unit. If the company can sell 10,000 units of Samoan Delight without incurring any additional fixed expenses:
a. Prepare a revised contribution format income statement that includes Samoan Delight. Assume that sales of the other two products does not change.
b. Compute the company’s revised break-even point in dollar sales. Also, compute its revised margin of safety in dollars and margin of safety percentage.
In: Accounting
Talk to me ~ Fear of public speaking is a common experience across many human cultures. To help people overcome this fear, researchers developed an internet-based telepsychology program for the treatment of this common social phobia. They recruit 44 people who meet a particular social phobia criterion to participate in a study and randomly assign them to either participate in the telepsychology program or to an in-person program with a therapist. At the end of the program, participants are evaluated and are considered "improved" if they no longer meet the social phobia criterion. Results from one iteration of the study are shown in the table below.
| Improved | Did Not Improve | Total | |
| Program 1: Telepsychology | 14 | 11 | 25 |
| Program 2: In-person | 12 | 7 | 19 |
| Total | 26 | 18 | 44 |
Round all numeric answers to four decimal places.
1. Calculate the observed difference in the proportion of participants in the telepsychology program and the in-person program that showed improvement, p^1−p^2p^1−p^2
2. Researchers want to determine if there is a
difference in results between the two programs, that is, is the
telepsychology program better than the in-person program or vice
versa? Or, are the two programs roughly the same? Choose the null
and alternative hypotheses that are appropriate to test this
research question.
A.
H0H0: There is no difference in the two treatment programs. The
observed difference in p^1−p^2p^1−p^2 is due to chance.
HAHA: There is a difference in the two treatment programs. The
observed difference in p^1−p^2p^1−p^2 is not due to chance.
B.
H0H0: There is no difference in the two treatment programs. The
observed difference in p^1−p^2p^1−p^2 is not due to chance.
HAHA: There is a difference in the two treatment programs. The
observed difference in p^1−p^2p^1−p^2 is due to chance.
C.
H0H0: There is a difference in the two treatment programs. The
observed difference in p^1−p^2p^1−p^2 is not due to chance.
HAHA: There is no difference in the two treatment programs. The
observed difference in p^1−p^2p^1−p^2 is due to chance.
D.
H0H0: There is a difference in the two treatment programs. The
observed difference in p^1−p^2p^1−p^2 is due to chance.
HAHA: There is no difference in the two treatment programs. The
observed difference in p^1−p^2p^1−p^2 is not due to chance.
3. The paragraph below describes the set up for a
randomization technique, if we were to do it without using
statistical software. Select an answer by choosing an option from
the pull down list or by filling in an answer in each blank in the
paragraph below:
To setup a simulation for this situation, we let each person be
represented with a card. We write Telepsychology on __________
cards and In-person on ________ cards. Then, we shuffle these cards
and split them into two groups: one group of size _________
representing those who improved, and another group of size
________representing those who did not improve. We calculate the
difference in the proportion of participants in the telepsychology
program and the in-person program, p^1,sim−p^2,simp^1,sim−p^2,sim.
We repeat this many times to build a distribution centered at the
expected difference of ___________ .
Lastly, we calculate the fraction of simulations where the
simulated differences in proportions are (lessthan/greater/beyond)
? less than greater than beyond the observed
difference.
In: Statistics and Probability
GRADED PROBLEM SET #5
Answer each of the following questions completely. There are a total of 20 points possible in the assignment.
In: Math
Terminal 5 (T5), built by British Airways for $8.6 billion, is London Heathrow Airport's newest state- of-the-art facility. Made of glass, concrete, and steel, it's the largest free-standing building in the United Kingdom and has more than 10 miles of belts for moving luggage. At the terminal's unveiling in March of 2008, Queen Elizabeth ll described the facility as an important of Britain’s future. Alas… the accolades didn't last long! After two decades in planning and 100 million hours in manpower, opening day didn't work out as planned. Endless lines and major baggage handling delays led to numerous flight cancellations stranding many irate passengers. Airport operators said the problems were triggered by glitches in the terminal's high-tech baggage-handling system.
With its massive automation features, T5 was planned to ease congestion at Heathrow and improve the flying experience for the 30 million passengers expected to pass through it annually. With 96 self-service check-in kiosks, more than 90fast check-in bag drops, 54 standard check-in desks, and miles of suitcase-moving belts estimated to be able to process 12,000 bags per hour, the facility's design seemed to support those goals.
However, within the first few hours of the terminal's operation, problems developed. Presumably understaffed, baggage workers were unable to clear incoming luggage fast enough. Arriving passengers waited more than an hour for their bags. Departing passengers tried in vain to check in for flights. Flights left with empty cargo holds. Sometime on day one, the airline checked in only those passengers with no luggage. And it didn't help that the moving belt system jammed at one point. Lesser problems also became apparent: a few broken escalators, some hand dryers that didn't work, a gate that wouldn't function at the new Underground station, and inexperienced ticket sellers who didn't know the fares between Heathrow and various stations on the Piccadilly line. By the end of the first full day of operation, Britain's Department of Transportation released a statement calling for British Airways and the airport operator BAA to get the problem fixed so customers would not be inconvenienced.
You might be tempted to think that all of this could have been prevented if British Airways had only tested the system. But thorough runs of all systems "from toilets to check in and seating" took place six months before opening, including four full-scale test runs using 16,000 volunteers.
Although T5’s debut was far from perfect, things have certainly changed. A recent customer satisfaction surveyshowed that 80 percent of passengers waited less than five minutes to check in. And those passengers are extremely satisfied with the terminal's lounges, catering, facilities, and ambience.
With the Summer Olympics in London, London’s Heathrow (and T5) grappled with a record passenger surge. As competitors, spectators, and media arrived. To cope with the deluge, some 1000 volunteers greeted arrivals, and special teams were assigned to deal with the athletes’’ oversize items like javelins, bikes, and other sports equipment. Despite the chaotic ‘birth’ of T5, it’s become a valued component of Heathrow and British Airways.
Please answer the following questions:
In: Operations Management
Body fluids were examined from Patients with a Chondrosarcoma over the time after initial treatment and remission. The levels of a particular chemotherapeutic drug were followed over a selected week. The "Nadir" or a minimum level was selected for analysis. Two weeks have been chosen for this analysis: one early in the treatment (Nadir 1); the other at the end of the treatment (Nadir 8)
Do the two nadirs differ? In particular, is Nadir 8 below Nadir 1? Use three test, one of which is parametric. Paired Data Problem
| Subject | NADIR 1 | NADIR 8 |
| 1 | 13.2 | 14 |
| 2 | 11.2 | 13.8 |
| 3 | 13.9 | 12.2 |
| 4 | 10.2 | 11.8 |
| 5 | 11.1 | 10.1 |
| 6 | 12.7 | 7.5 |
| 7 | 12 | 11.6 |
| 8 | 9.3 | 10.4 |
| 9 | 12.9 | 11.5 |
| 10 | 12.8 | 11.5 |
| 11 | 11.6 | 9.2 |
| 12 | 10.8 | 9.6 |
| 13 | 11.2 | 11.6 |
| 14 | 14.2 | 11.2 |
| 15 | 10.8 | 11.6 |
| 16 | 12.3 | 11.4 |
| 17 | 12.4 | 10.9 |
| 18 | 11.1 | 10.2 |
| 19 | 12.4 | 12.5 |
| 20 | 11.4 | 10.5 |
| 21 | 11.2 | 10.5 |
| 22 | 11.2 | 8.4 |
| 23 | 11.9 | 8.6 |
| 24 | 12.6 | 12 |
| 25 | 11.5 | 12.9 |
| 26 | 12 | 12 |
| 27 | 10.8 | 12 |
| 28 | 11.1 | 10.5 |
| 29 | 12 | 9.4 |
| 30 | 11.7 | 12 |
In: Statistics and Probability
Answer the following questions. Please show your work or otherwise justify your answers. If you’re asked to create a truth table, show the entire table.
Create the truth table for the statement form: ~(? → ?) ↔ (? ∧ ~?)
Write the two statements in symbolic form and determine if they’re equivalent. Construct a full truth table, and explain how this shows equivalency (or a lack thereof). Statement 1: If you play aggressively and protect your king, then you will win the match. Statement 2: You didn’t play aggressively or you didn’t protect your king or you won the match.
In: Advanced Math
A school is conducting optimization studies of the resources it has. One of the principal concerns of the Director is that of the staff. The problem he is currently facing is with the number of guards in the "Emergencies" section. To this end, he ordered a study to be carried out that yielded the following results:
Time Minimum number of guards required O to 4 40 4 to 8 80 8 to 12 100 12 to 16 70 16 to 20 120 20 to 24 50 Each guard, according to Federal labor law, must work eight consecutive hours per day. Formulate the problem of hiring the minimum number of guards that meet the above requirements, as a Linear programing model.
In: Advanced Math