An operations analyst in a sheriff's department studied how frequently their emergency helicopter was used during the past year, by time of day (shift 1 2AM-8AM, shift 2 8AM-2PM, shift 3 2PM-8PM, shift 4 8PM-2AM) Random samples of size 16 for each shift were obtained. The dependent variable (freq) and the categorical variable (shift) .

Use transformation if necessary using the Box-Cox method that satisfies one way ANOVA model (State whether your transformation is valid or not). The data is attached.

It is known that 72.3% of statistics students do their homework in time for it to be collected and graded. Each student does homework independently. Students are selected randomly. In a statistics class of 44 students, a. what is the probability that at least 29 students will do their homework on time? Use the binmial probability formula. Round your answer to 3 decimals. b. what is the probability that exactly 31 will do their homework on time? Use the binomial probability formula. Round your answer to 3 decimals.

                                                      
The labor quotation department at Excabar, a large manufacturing company, wants to verify the accuracy of their labor bidding process (estimated cost per unit versus actual cost per unit). They have randomly chosen 35 product quotations that subsequently were successful (meaning the company won the contract for the product). The data is presented to the left of this text.                                                      
                                                      
                                                      
                                                      
                                                      
1. Set up the hypotheses to test whether the Estimated cost/unit is significantly different than the Actual cost/unit.                                                      
                                                      
2. Using the appropriate commands in Excel, find the value of the test statistic. Assume the populations variances are unknown but equal. Compute the 99% Confidence Interval for each variable.                                                      
                                                      
                                                      
3. Interpret the p- value at α = .01                                                      
                                                      
4. Based on these results, write a statement expressing the results of this study.                                                      
                                                      
Null:   μ      μ                                          
Alternative:   μ      μ                                          

Product   Estimated cost/unit   Actual cost/unit
1   13.90   12.90
2   18.80   15.80
3   14.80   11.80
4   11.80   11.80
5   16.80   12.80
6   14.20   13.20
7   21.80   18.80
8   6.80   10.80
9   19.50   18.50
10   21.00   19.00
11   12.40   11.40
12   15.10   18.10
13   15.80   15.80
14   24.90   23.90
15   13.20   16.20
16   25.90   23.90
17   12.80   10.80
18   12.90   11.90
19   20.50   19.50
20   19.00   18.00
21   10.80   10.80
22   10.80   13.80
23   18.80   17.80
24   12.60   11.60
25   26.80   22.80
26   22.90   24.90
27   22.80   19.80
28   12.50   16.50
29   15.50   15.50
30   14.10   13.10
31   15.10   19.10
32   12.50   10.50
33   21.90   22.90
34   24.20   20.20
35   17.80   14.80

Heat treating is often used to carburize metal parts, such as gears. The thickness of the carburized layer is considered a crucial feature of the gear and contributes to the overall reliability of the part. Because of the critical nature of this feature, two different lab tests are performed on each furnace load. One test is run on a sample pin that accompanies each load. The other test is a destructive test, where an actual part is cross-sectioned. This test involves running a carbon analysis on the surface of both the gear pitch (top of the gear tooth) and the gear root (between the gear teeth). Table 12-6 shows the results of the pitch carbon analysis test for 32 parts.

PLEASE answer only the STEPWISE part of the question

except utilize stepwise regression to identify a model.]

1. Fit a regression model using all five regressors except utilize stepwise regression to identify a model. Write out the equation. Summarize this analysis by providing the equation, ?², and list the standard errors.    What does the analysis of variance indicate?
2. Check for multicollinearity for stepwise regression . Explain your findings.
3. Describe what you notice about the p values for the regressors. Construct a t-test on each regression coefficient. What can you conclude about the variables in this model? Use an alpha = 0.05 for stepwise regression
4. Prepare a normal probability plot of the residuals and check the adequacy of the model for stepwise regression

Lisa Monnin is the budget director at Nexos Media, Inc. She wants to compare the daily expenses of diets of the sales staff with the expenses of the audit staff, for which she compiled the following information about the samples. Sales ($) 845 826 827 875 784 809 802 820 829 830 842 832 Audit ($) 841 890 821 771 850 859 825 829 If we assume that the standard population deviations are equal and at a significance level of 0.10, can Monnin conclude that the average daily expenses of sales personnel are greater than those of the audit staff? What is the value of p?

Six textbooks are to be arranged on a shelf. In how many ways can they be arranged?

A) 6p4 360 ways

B) 6p3 120 ways

C) 6c6 1 way

D) 6p6 720 ways

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.94. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $0.25 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95% confidence. (Round your answers up to the nearest whole number.)

The desired margin of error is $0.10.

(b)

The desired margin of error is $0.06.

(c)

The desired margin of error is $0.04.

A female employee at a nearby hospital is convinced that male physicians are earning significantly more of an annual salary than female physicians. In order to test the hypothesis that male physicians earn more than $15,000.00 on the average than females, the employee gathers a SRS of male and female physicians at the health center. Assume the following table summarizes the descriptive statistics for the two groups.

A) Carry out the appropriate statistical procedure to test the employee’s hypothesis at the alpha=0.05 level. Do not assume equal variances. Carefully write out your null and alternative hypotheses, and interpret your results.

B) Construct a 95% confidence interval about your point estimate for the difference in annual income by gender. Provide an interpretation for your confidence interval.

Money reports that the average annual cost of the first year of owning and caring for a large dog in 2017 is $1,448. The Irish Red and White Setter Association of America has requested a study to estimate the annual first-year cost for owners of this breed. A sample of 50 will be used. Based on past studies, the population standard deviation is assumed known with σ = $260.

1,902 2,042 1,936 1,817 1,504 1,572 1,532 1,907 1,882 2,153 1,945 1,335 2,006 1,516 1,839 1,739 1,456 1,958 1,934 2,094 1,739 1,434 1,667 1,679 1,736 1,670 1,770 2,052 1,379 1,939 1,854 1,913 2,163 1,737 1,888 1,737 2,230 2,131 1,813 2,118 1,978 2,166 1,482 1,700 1,679 2,060 1,683 1,850 2,232 2,294

(a) What is the margin of error for a 95% confidence interval of the mean cost in dollars of the first year of owning and caring for this breed? (Round your answer to nearest cent.) $

(b) The DATAfile Setters contains data collected from fifty owners of Irish Setters on the cost of the first year of owning and caring for their dogs. Use this data set to compute the sample mean. Using this sample, what is the 95% confidence interval for the mean cost in dollars of the first year of owning and caring for an Irish Red and White Setter? (Round your answers to nearest cent.)

Recent publications have hinted at the growing importance of sleep in the elderly in order to maintain good health. Suppose a researcher is interested in the hypothesis that the difference in average hours of sleep differs significantly between men aged 35-45 and men aged 45+. Assume the following table summarizes the descriptive statistics for SRSs from each age group. Carry out the appropriate statistical test to answer the researcher’s hypothesis regarding the difference in average hours of sleep between the two groups under investigation. Assume that all conditions for the testing are met. Use an alpha level of 0.05. Calculate a pooled variance under the equal variance assumption. Write out your null and alternative hypotheses and interpret your pvalue.

2.5 points   

In the file pubexp.dat there are data on public expenditure on education (EE), gross

domestic product (GDP), and population (P) for 34 countries in the year 1980. It is

hypothesized that per capita expenditure on education is linearly related to per capita

GDP. That is,

yi . b1 . b2xi . ei

where

yi . EEi

Pi

and xi . GDPi

Pi

It is suspected that ei may be heteroskedastic with a variance related to xi.

(a) Why might the suspicion about heteroskedasticity be reasonable?

(b) Estimate the equation using least squares; plot the least squares function and the

residuals. Is there any evidence of heteroskedasticity?

(c) Test for the existence of heteroskedasticity using a White test.

(d) Use White’s formula for least squares variance estimates to find some alternative

standard errors for the least squares estimates obtained in part (b). Use

these standard errors and those obtained in part (b) to construct two alternative

95% confidence intervals for b2. What can you say about the confidence interval

that ignores the heteroskedasticity?

(e) Reestimate the equation under the assumption that var.ei. . s2xi. Report the

results. Construct a 95% confidence interval for b2. Comment on its width

relative to that of the confidence intervals found in part (d).

Two basketball players on a school team are working hard on consistency of their performance. In particular, they are hoping to bring down the variance of their scores. The coach believes that the players are not equally consistent in their games. Over a 10-game period, the scores of these two players are shown below. Assume that the two samples are drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: chi-square table or F table)

Click here for the Excel Data File

a. Select the hypotheses to test whether the players differ in consistency.

• H₀: σ₂² / σ₁² = 1, H_A: σ₂² / σ₁² ≠ 1.

• H₀: σ₂² / σ₁² ≥ 1, H_A: σ₂² / σ₁² < 1.

• H₀: σ₂² / σ₁² ≤ 1, H_A: σ₂² / σ₁² > 1.

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c-1. Find the p-value.

• p-value 0.10
• 0.05 p-value < 0.10
• 0.02 p-value < 0.05
• 0.01 p-value < 0.02

• p-value < 0.01

c-2. At α = 0.05, what is your conclusion?

• Do not reject H₀; we can say that consistency differs between the players

• Reject H₀; we cannot say that the consistency differs between the players

• Reject H₀; we can say that consistency differs between the players

• Do not reject H₀; we cannot say that consistency differs between the players

In a survey, an Institute discovered that 40% of people who responded couldn’t remember any of the laws by the First Amendment. You decide to build a distribution for how many respondents could not recall any of the laws. You take on a random sample of 10 Americans.

A. What are the assumptions of a binomial distribution? Does the example match the assumptions?

B. What is the probability that the sample has exactly n successes, for n=1,2,3…10?

C. Plot the probabilities that were calculated in B.

D. Find the probability that the sample has at least 5 successes.

E. Find the probability that the sample has at most 3 successes.

Read article “Coronavirus vaccine trials: Chinese volunteers recount their experiences” Then explain, in detail, how you would design the experiment to test the vaccine and then how you would analyze the data after the experiment. If you simply repeat the information from the article, you’ll get no 3 credit (I’ve read the article). So you must offer useful information beyond (not mentioned in) the article. Use table or graph if necessary. There is no unique correct answer so your grade depends the quality of your answer. Limit your answer to one page.

108 people aged 18-60 from Wuhan have been injected with a potential vaccine developed by a Chinese pharmaceutical firm and the military. One says that by taking part she can ‘rise above the simple interests of a normal person for once’

There may have been diarrhoea, high temperatures and a fair bit of apprehension, but 108 people from Wuhan can proudly say that this week they became the first in the country to be injected with a possible vaccine for the novel coronavirus.

The trials got under way in the central China city on Thursday, just three days after CanSino Biologics – the pharmaceutical company that developed the product in cooperation with the Chinese military – was given the green light by Beijing.

According to information published on China’s clinical trial registry, the volunteers – aged from 18 to 60 and in good health – were divided into three groups of 36 and then given either a low, medium or high dose of the vaccine at a facility owned by the city’s armed police force.

In a report by Science Daily, Wang Junzhi, a fellow at the Chinese Academy of Engineering, said that after receiving their injections, the participants would spend 14 days in quarantine under close medical observation.

In a rare move, some of the volunteers took to social media to recount their experiences to the public.

“I was a bit fearlessly naive when I signed up,” said a young woman with the nickname Xiao Mi, who was in the low dosage group.

“It only took a day from me being notified to getting the injection,” she said on Weibo, China’s Twitter-like platform.

Xiao said she read up about the possible side-effects, like allergic reactions, online and was scared after receiving her shot. But that was “probably the worst thing”, she said.

“Two people from our batch saw their body temperatures rise to 38 degrees … and some had diarrhoea,” she said, adding that all of the side-effects passed quite quickly.

What was more important, Xiao said, was that although she was apprehensive, by taking part in the trials she felt she was doing her bit for society.

“I feel I can bear the consequences,” she said. “I want to rise above the simple interests of a normal person for once. We should be thanking all those who have stood in front of normal people.”

Xiao also confirmed earlier reports that the first person to receive a shot of the possible vaccine was Chen Wei, a major general and military scientist
who is also heading up the trial.

Another of the volunteers was Li Ming, whose wife, Wang Feng, recently recovered from a relatively mild case of Covid-19 – the disease caused by the coronavirus.

“From the onset of symptoms until now, I have experienced a lot of difficulties in getting a diagnosis and treatment,” Wang was quoted as saying in the Science Daily report.

“My husband has accompanied me through this, and he fully understands how difficult it is for a patient.”

Wang Junzhi said that the development programmes appeared to be going well and that most of the research teams should be able to complete their preclinical studies by next month and proceed to clinical trials soon after.

However, Roy Hall, a virology professor at the University of Queensland in Australia, said that even if vaccine trials were fast-tracked, it would still be some time before a vaccine was ready to go into mass production.

“It may be available within six to nine months of starting clinical trials, he said. “So that would mean a vaccine becomes available within a year of discovering the pathogen. That would be a remarkable achievement.”

Consider a computer technical support center where personnel take calls and provide service. The time between calls ranges from 1 to 4 minutes. There are two technical support people – Ayşe and Burak. Ayşe is more experienced and can provide service faster than Burak. System works as follows:

• Ayşe takes the call if both technical support are idle.
• If Ayşe is busy and Burak is idle, Burak takes the call.
• If both Ayşe and Burak are busy, call waits in a queue until one of them gets idle.

Simulate the system for 8 calls. Interarrival distribution of calls and service time distributions for Ayşe and Burak are provided below.

Given that the first arrival occurs at time t = 0, create a record of hand simulation (on the empty table given below) and compute the following performance measures:

1. Average waiting time per customer
2. Average time in system
3. Average service time
4. Average interarrival time
5. Utilization of Ayşe
6. Utilization of Burak
7. Average number of customers in queue
8. Average number of customers in system

In the “when Ayşe becomes available” and “when Burak becomes available” columns you can write the time when Ayşe/Burak becomes available in order to make the simulation easier for you. In the first call, since both servers are idle, Ayşe takes the call.