give example for a static mathematical model?

Describe how the researcher should apply the five basic steps in a statistical study. ( Assume that all the people in the poll answered truthfully).

The percentage of workers that drink coffee or tea

a. The population is all workers. The researcher wants to estimate the percentage in this population that do not drink coffee or tea.

B. The population is all workers. The researcher wants to estimate the percentage in this population that drink coffee or tea.

C. The population is all workers that do not drink coffee or tea. The researcher wants to estimate the number in this population that drink coffee or tea.

D. The population is all workers that drink coffee or tea. The researcher wants to estimate the number in this population that drink coffee or tea.

Determine how to apply the second basic step in a statistical study in this situation.

A. The researchers should only gather raw data from workers that drink coffee or tea.

B. the researcher should gather data about drinking coffee or tea from the largest sample of workers from which the researcher can gather data.

C. the researcher should only gather raw data from workers that do not drink coffee or tea

D. the researcher should gather raw data from all the workers about whether or not they drink coffee or tea.

Determine how to apply the third step in the statistical study in this situation:

A. the sample statistic of interest is the number of workers in the sample that do not drink coffee or tea.

B. The sample statistic of interest in the percentage of workers in the sample that do not drink coffee or tea

C. the sample statistic of interest is the percentage of workers in the sample that drink coffee or tea

D. the sample statistic of interest is the number of workers in the sample that drink coffee or tea

Determine how to apply the fourth basic step in the statistical study in this situation.

A. If the researcher followed correct procedures, he or she can be confident that the sample statistics is equal to the percentage of workers in the population that drink coffee or tea

B. the researcher should use the sample statistic as an estimate for the population value of the percentage of workers that drink coffee or tea and then use the methods of statistics to determine how good that estimate is.

C. If the percentage of workers that drink coffee or tea is greater than 50% in the sample, the researcher can be confident that all workers drink coffee or tea

D. The sample statistics provides no useful information to the researcher in this situation

Determine how to apply the fifth basic step in the statistical study in this situation.

A. the researcher should use the methods of the statistics to determine the quality of the estimate of the population parameter and draw conclusions based on this estimate accordingly.

B. the researcher knows that the sample static is equal to the population parameter, so he or she may draw conclusion with complete confidence.

C. there is no way to determine how well the sample statistic estimates the population parameter,

D. the researcher cannot draw any conclusion based on the value of the sample statistic.

According to one survey taken a few years ago, 32% of American households have attempted to reduce their long-distance phone bills by switching long-distance companies. Suppose that business researchers want to test to determine if this figure is still accurate today by taking a new survey of 80 American households who have tried to reduce their long-distance bills. Suppose further that of these 80 households, 22% say they have tried to reduce their bills by switching long-distance companies. Is this result enough evidence to state that a significantly different proportion of American households are trying to reduce long-distance bills by switching companies? Let α = .01.

Suppose 5 of 25 Ford subcompact automobiles require adjustment of some kind. Four subcompacts are selected at random. We are interested in the probability that exactly one will require adjustment. a. Solve the problem assuming that of the 25 subcompacts, the samples are drawn without replacement. b. Solve the problem assuming the sampling is done with replacement c. Assuming the replacement, work the problem using the Poisson distribution.

the shape of the distribution of the time required to get an oil change at a 20​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 21.2 minutes​, and the standard deviation is 3.4 minutes.

Complete parts ​(a) through (c).

​(a) To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required?

​(b) What is the probability that a random sample of n=45 oil changes results in a sample mean time less than 20 ​minutes?

​(c) Suppose the manager agrees to pay each employee a​ $50 bonus if they meet a certain goal. On a typical​ Saturday, the​ oil-change facility will perform 45 oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample, there would be a​ 10% chance of the mean​ oil-change time being at or below what​ value? This will be the goal established by the manager.

Assume a normal distribution of the form N(100, 100), answer the following questions:

What proportion of the distribution falls within 1 standard deviation of the mean (e.g., within -1 and 1 standard deviation)?

What is the probability of a single draw from that distribution has a value greater than 115?

What is the range that captures the middle 95% of the population distribution?

If I randomly sample 10 observations from this distribution and calculate a mean, what is the probability that this mean is greater than 106?

If we center the sampling distribution on 100, then what is the range that will capture 95% of the means calculated from a sample of 20 observations?

The yield of a chemical process is being studied. The two most important variables are thought to be the pressure and the temperature. Three levels of each factor are selected, and a factorial experiment with two replicates is performed. The yield data are as follows:

1. Use the LSD test to determine which levels of the pressure factor are significantly different.
2. Use the LSD test to determine which levels of the temperature factor are significantly different.
3. Suppose that we wish to reject the null hypothesis with a high probability if the difference in the true mean yield at any two pressures is as great as 0.5. If a reasonable prior estimate of the standard deviation of yield is 0.1, how many replicates should be run?

Test if the population mean price for clarity “VS1” is different than that for clarity “VVS1 or VVS2”.

Please answer with R programming code

Question 15.

What are the three required assumptions for the appropriate use of the independent groups t-test? What are the three required assumptions for the appropriate use of the dependent groups t-test?Can you use these tests when you have three groups? What test do we use instead? Can the dependent variable be nominal? What should the nature of the dependent variable be?

A team of health research wants to investigate whether having regular lunch break improves working adults’ sleep. A group of 85 adults with a full-time job were recruited in the study, they reported average hours of sleep in the past week, committed to having a 1-hour, out-of-office, work-free lunch break each day for 3 months, and, at the end of the study, reported average hours of sleep in the past week. The mean difference in hours of sleep before and after the study was 3 with a standard deviation of 0.9. Which one of the following statements is INCORRECT? (Set alpha level at 0.05.)

We have 95 students in a class. Their abilities/eagerness are uniform randomly distributed on a scale between 1 and 4; and at the end of the class they will be judged right and they will receive a grade corresponding to their ability/eagerness (corresponding to their performance). What is the probability that the class average will be between 2.8 and 4? How would this number change (if it does) for 120 students?

(PLEASE, SINCE THE VERY BEGINNING, ALL THE ONE BY ONE STEPS NEED TO BE MENTIONED IN YOUR CALCULATION) A manufacturer of cell phones guarantees that his cell phones will last, on average, 3 years with a standard deviation of 1 year. If 5 of those cell phones are found to have lifetimes of 1.9, 2.4, 3.0, 3.5 and 4.2 years, can the manufacturer still be convinced that his cell phones have a standard deviation of 1 year? Test at a 0.05 level of confidence. Thank you in advance for your help!

Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made the time period of January 1 to March 31. Table #11.2.4 gives the defect and the number of defects.

Table #11.2.4: Number of Defective Lenses

Do the data support the notion that each defect type occurs in the same proportion? Test at the 10% level.

The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site.

Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are the same.
H₁: The distributions are the same.

H₀: The distributions are the same.
H₁: The distributions are different.    

H₀: The distributions are different.
H₁: The distributions are different.

H₀: The distributions are different.
H₁: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

normal

Student's t    

binomial

uniform

chi-square

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 0.01 level of significance, the evidence is sufficient to conclude that the regional distribution of raw materials does not fit the distribution at the current excavation site.

At the 0.01 level of significance, the evidence is insufficient to conclude that the regional distribution of raw materials does not fit the distribution at the current excavation site.

Use the data in the file andy.dta consisting of data on hamburger franchises in 75 cities from Big Andy's Burger Barn.

Set up the model

ln(Si)=b1 + b2ln(Ai) + ei,

where

Si = Monthly sales revenue ($1000s) for the i-th firm

Ai = Expenditure on advertising ($1000s) for the i-th firm

(a) Interpret the estimates of slope and intercept.

(b) How well did the model fit to the data? Use any tests and measures presented in class.

(c) Perform any test for heteroscedasticity in your data.