A recent study on state income tax payments found that the average person paid $7,500 each year with a standard deviation of $250.20. After multiple propositions by local experts, a change was implemented to reduce this tax burden. Suppose a random sample of 240 people was taken after the proposed changes and these individuals exhibited a mean tax payment of $7,425.

1. What would a 95% confidence interval for the population mean be? [Show your code in “R Code” section. Show the answer in “Answer” section. Leave “Comments” section blank.]
2. What would it suggest with regards to whether they have properly reduced the tax burden? Why? [Leave “R Code” and “Answer” sections blank. Include the phrase “reduced” or “did not reduce” along with a justification in a few sentences in “Comments” section.]

Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first gives the animal a tranquilizer shot. The effect of the shot is supposed to last an average of 65 minutes, and it usually does. However, Jim sometimes gets chased out of the pasture by a bull that recovers too soon, and other times he becomes worried about prize bulls that take too long to recover. By reading journals, Jim has found that the tranquilizer should have a mean duration time of 65 minutes, with a standard deviation of 15 minutes. A random sample of 14 of Jim's bulls had a mean tranquilized duration time of close to 65 minutes but a standard deviation of 23 minutes. At the 1% level of significance, is Jim justified in the claim that the variance is larger than that stated in his journal? Find a 95% confidence interval for the population standard deviation.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² > 225; H₁: σ² = 225

H_o: σ² = 225; H₁: σ² ≠ 225    

H_o: σ² = 225; H₁: σ² < 225

H_o: σ² = 225; H₁: σ² > 225

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a uniform population distribution.

We assume a normal population distribution.    

We assume an exponential population distribution.

We assume a binomial population distribution.

(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?

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 1% level of significance, there is insufficient evidence to conclude that the variance of the duration times of the tranquilizer is larger than stated in the journal.

At the 1% level of significance, there is sufficient evidence to conclude that the variance of the duration times of the tranquilizer is larger than stated in the journal.    

(f) Find the requested confidence interval for the population standard deviation. (Round your answers to two decimal place.)

Interpret the results in the context of the application.

We are 95% confident that σ lies within this interval.

We are 95% confident that σ lies above this interval.    

We are 95% confident that σ lies below this interval.

We are 95% confident that σ lies outside this interval.

A sports team compared two versions of a basketball (denoted as J and K) with respect to the time it takes to reach the hoop when thrown. They randomly selected 100 basketball players, and then they randomly assigned 50 to each basketball version. Basketball J has a sample mean of 209 and an SD of 37, while Basketball K has a sample mean of 225 and an SD of 41. It is known that the population variances are equal.

The sports team wants to know if there’s a significant difference between the two basketball versions with regards to the mean time they take to reach the hoop. To answer this, compute a 95% confidence interval for the difference in the mean time for the two basketball versions (J and K), and state hypothesis and conclusion

*Please don't copy other experts' solution

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Temperature 50°C 60°C 70°C 30 29 28 20 30 33 32 33 33 35 22 35 28 26 36 a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total b. Use a level of significance to test whether the temperature level has an effect on the mean yield of the process. Calculate the value of the test statistic (to 2 decimals). The p-value is What is your conclusion?

If you have a two tailed test with 10df, your rejection value will be _____________.

Group of answer choices

+2.228 and -2.228

+1.182 and -1.182

only +2.228

only +1.182

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Question 22 pts
If you have a 1 tailed, lower tail test with 20df, your rejection value will be _____________.

Group of answer choices

-2.086

-1.725

+1.725

+2.086

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Question 32 pts
As your sample size becomes large enough so that you have more than 120df, your t-distribution will approximate a normal distribution.

Group of answer choices

True

False

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Question 42 pts
When you have more than 120df, your rejection value for a one-tail, upper tail test will be +1.645.

Group of answer choices

True

False

Flag this Question
Question 52 pts
The t-distribution is a normal, unimodal and summetrical distribution.

Group of answer choices

True

False

I need it in 20 minutes time kindly

Suppose that we have a red coin and a blue coin. The red coin has probability pR = 0.1 of landing heads, and the blue coin has probability pB = 0.2 of landing heads.

(a) Write R code to generate a sequence of coin tosses, starting with the red coin, and switching coins every time a coin lands heads.

(b) Generate 1000 such sequences, each consisting of 1000 coin tosses, and use them to construct a plot of the 2.5%, 50% and 97.5% quantiles of the proportion of red coins tossed as the number of tosses increases. (c) What is the stationary distribution of colours for this process? Comment on how this experiment relates to Birkhoff’s ergodic theorem

The Capital Asset Price Model (CAPM) is a financial model that attempts to predict the rate of return on a financial instrument, such as a common stock, in such a way that it is linearly related to the rate of return on the overal market. Specifically,

RStockA,i = β0 + β1RMarket,i + ei

You are to study the relationship between the two variables and estimate the above model:

iRStockA,i - rate of return on Stock A for month i, i=1,2,⋯59.

iRMarket,i - market rate of return for month ii, i=1,2,⋯,59

β1 represent's the stocks 'beta' value, or its systematic risk. It measure's the stocks volatility related to the market volatility. β0 represents the risk-free interest rate.

The data in the  file contains the data on the rate of return of a large energy company which will be referred to as Acme Oil and Gas and the corresponding rate of return on the Toronto Composite Index (TSE) for 59 randomly selected months.

Therefore RAcme,i represents the monthly rate of return for a common share of Acme Oil and Gas stock; RTSE,i represents the monthly rate of return (increase or decrease) of the TSE Index for the same month, month ii. The first column in this data file contains the monthly rate of return on Acme Oil and gas stock; the second column contains the monthly rate of return on the TSE index for the same month.

(a) Use software to estimate this model. Use four-decimals in each of your least-squares estimates your answer.


RAcme,i^ = ____+____RTSE,i

(b) Find the coefficient of determination. Expresses as a percentage, and use two decimal places in your answer.

r2=

(c) In the context of the data, interpret the meaning of the coefficient of determination.

A. There is a strong, positive linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE Index.
B. There is a weak, positive linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE Index.
C. The percentage found above is the percentage of variation in the monthly rate of return of the TSE Index that can be explained by its linear dependency with the monthly rate of return of Acme stock.
D. The percentage found above is the percentage of variation in the monthly rate of return of Acme stock that can be explained by its linear dependency with the monthly rate of return of the TSE Index.


(d) Find the standard deviation of the prediction/regression, using two decimals in your answer.

Se =

(e, i) You wish to test if the data collected supports the statistical model listed above. That is, can the monthly rate of return on Acme stock be expressed as a linear function of the monthly rate of return on the TSE Index? Select the correct statistical hypotheses which you are to test.

A. H0:β0=0HA:β0≠0H0:β0=0HA:β0≠0
B. H0:β1=0HA:β1≠0H0:β1=0HA:β1≠0
C. H0:β1=0HA:β1>0H0:β1=0HA:β1>0
D. H0:β1=0HA:β1<0H0:β1=0HA:β1<0
E. H0:β0=0HA:β0>0H0:β0=0HA:β0>0
F. H0:β1≠0HA:β1≠0H0:β1≠0HA:β1≠0
G. H0:β0=0HA:β0<0H0:β0=0HA:β0<0
H. H0:β0≠0HA:β0≠0H0:β0≠0HA:β0≠0

(e, ii) Use the FF-test, test the statistical hypotheses determined in (e, i). Find the value of the test statistic, using three decimals in your answer.

Fcalc =

(e, iii) Find the P-value of your result in (e, ii). Use three decimals in your answer.

P-value =

(f) Find a 95% confidence interval for the slope term of the model, β1.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)


(h) Find a 95% confidence interval for the β0 term of the model.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)


(k) Last month, the TSE Index's monthly rate of return was 1.5%. This is, at the end of last month the value of the TSE Index was 1.5% higher than at the beginning of last month. With 95% confidence, find the last month's rate of return on Acme Oil and Gas stock.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)

What is St. Petersburg paradox, you have to show what it is, what kind of problem it comes with, how this problem can be solved, and how the utility could solve this problem.

Background: Anorexia is well known to be difficult to treat. The data set provided below contains data on the weight gain for three groups of young female anorexia patients. These groups include a control group, a group receiving cognitive behavioral therapy and a group receiving family therapy. Source: Hand, D. J., Daly, F., McConway, K., Lunn, D. and Ostrowski, E. eds (1993) A Handbook of Small Data Sets. Chapman & Hall, Data set 285 (p. 229).

Directions: Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it. Then perform an analysis of variance (ANOVA) to determine whether or not the differences in weight gain between the treatment groups is statistically significant.

Data

1. State the null and alternative hypotheses.
   
   
   
2. Compute the test statistic. Document how SSTr and SSE were computed. Use 4 decimal places for the sample means, sample standard deviations and the grand mean and round your answers for SSTr and SSE to 2 decimal places.
   
   Use the values for SSTr and SSE to complete the following ANOVA table. Round each of your answers to 2 decimal places.
   

   Source	S.S.	df	M.S.	F
   Treatment
   Error
   Total

3. Compute the p-value. Provide the name of the distribution and the parameters used to compute the p-value. Then enter your answer rounded to 4 decimal places.
   
   
   
4. Interpret the results of the significance test. Is this result statistically significant? Is this result important from a practical perspective?
   

Your foreman claims that tree planting is a job for young people. He further claims that 3/4 of tree planters are below the age of 21. You think he's exaggerating and the proportion of tree planters under 21 is not nearly that high. You gain access to a page from the personnel files that has the birthdates for 50 tree planters and count 32 who are under 21. Do you have enough evidence (at α=.05) to conclude that your foreman is wrong and that the proportion of tree planters under 21 is less than 3/4?

A machine can be adjusted so that, when it is under control, the mean amount of sugar dispensed is 5 lbs. It is known that the population standard deviation is .15 lbs. The quality control supervisor would like to know if the quality is controlled. To do a quality control check, 16 bags of sugar are randomly selected and weighed. The sample mean was found to be 5.1 lbs. Find the p-value for this test rounded to 4 decimal places

A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance σ² = 42.3. In a different section of Chaco Canyon, a random sample of 20 transects gave a sample variance s² = 48.7 for the number of sites per transect. Use a 5% level of significance to test the claim that the variance in the new section is greater than 42.3. Find a 95% confidence interval for the population variance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 42.3; H₁: σ² > 42.3

H_o: σ² = 42.3; H₁: σ² < 42.3    

H_o: σ² = 42.3; H₁: σ² ≠ 42.3

H_o: σ² > 42.3; H₁: σ² = 42.3

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a normal population distribution.

We assume an exponential population distribution.    

We assume a binomial population distribution.

We assume a uniform population distribution.

(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?

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 5% level of significance, there is insufficient evidence to conclude that the variance is greater in the new section.

At the 5% level of significance, there is sufficient evidence to conclude that the variance is greater in the new section.    

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Interpret the results in the context of the application.

We are 95% confident that σ² lies above this interval.

We are 95% confident that σ² lies within this interval.    

We are 95% confident that σ² lies below this interval.

We are 95% confident that σ² lies outside this interval.

Consider the data set: 26, 29, 24, 17, 27, 20, 23, 21, 26, 27.

(a) Find the median and the upper and lower quartiles for this data set.

(b) Setup then evaluate the numerical expression for the mean of this data set. You must write it out completely. (

c) Setup and then evaluate the numerical expression for the variance of this data set. You must write it out completely.

(d) Find the standard deviation of this data set.

Thirty randomly selected students took the calculus final. If the sample mean was 75 and the standard deviation was 7.2​, construct a​ 99% confidence interval for the mean score of all students.