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 26 transects gave a sample variance s2 = 47.3 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.

Ho: σ2 = 42.3 ;H1: σ2 < 42.3

Ho: σ2 = 42.3; H1: σ2 ≠ 42.3

Ho: σ2 > 42.3; H1: σ2 = 42.3

Ho: 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 binomial population distribution.

We assume a exponential population distribution.

We assume a normal 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 conclude that the variance is greater in the new section.

At the 5% level of significance, there is sufficient evidence to conclude 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.)

lower limit

upper limit

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 outside this interval.

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

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

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 24 transects gave a sample variance s² = 49.1 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 uniform population distribution.

We assume a normal population distribution.    

We assume a binomial population distribution.

We assume a exponential 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 conclude that the variance is greater in the new section.

At the 5% level of significance, there is sufficient evidence to conclude 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 within this interval.

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

We are 95% confident that σ² lies outside this interval

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

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.

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 18 transects gave a sample variance s² = 49.7 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 uniform population distribution.We assume a binomial population distribution.    We assume a normal population distribution.We assume a exponential 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 conclude that the variance is greater in the new section.

At the 5% level of significance, there is sufficient evidence to conclude 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 within this interval.

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

  We are 95% confident that σ² lies above this interval

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

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 19 transects gave a sample variance s² = 48.5 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 a uniform population distribution.    

We assume a binomial population distribution.We assume a exponential 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 conclude that the variance is greater in the new section.

At the 5% level of significance, there is sufficient evidence to conclude 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 below this interval.

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

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

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

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 = 46.5 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 exponential population distribution. We assume a normal 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 conclude that the variance is greater in the new section. At the 5% level of significance, there is sufficient evidence to conclude 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 outside this interval. We are 95% confident that σ² lies above this interval.     We are 95% confident that σ² lies below this interval. We are 95% confident that σ² lies within this interval.

1.Give the reason why sound waves can go around most of objects.

2. Give the reason why most of objects block light waves.

3. From the video, what is the correction about the speed of red light compare with the one of the purple light?

4. Explain why waves going through a larger hole will not spared as much and move forward as going through a smaller hole?

Python Programming

Revise the ChatBot program below. There needs to be one list and one dictionary for the ChatBot to use. Include a read/write function to the program so that the program can learn at least one thing and store the information in a text document.

ChatBot program for revising:

# Meet the chatbot Eve

print('Hi there! Welcome to the ChatBot station. I am going to ask you a series of questions and all you have to do is answer!')

print(' ')

print('Lets get started')

#begin questions

firstName = input('What is your first name?: ')

lastName = input('What is your last name? ')

print("Hi there, ", firstName + lastName, "nice to meet you")

print(" ")

# questions about users favorite things

currentYear = 2020

birthDay = input('What is the year were you born?: ')

birthDay = int(birthDay)

print('Wow! You are already', currentYear - birthDay)

print(" ")

# questions about favorite hobbies

firstHobby = input('Do you play any sports? ')

if(firstHobby == 'Yes'):

sport = input('What sport do you play? ')

print("Nice! I played Soccer and Tennis back when I was human")

print(" ")

else:

print("Bummer, I always liked sports")

print(" ")

favAnimal = input('What is your favorite animal? ')

print("Oooohhh what a cool animal! My favorite is the red panda, such a unique and cute species!")

print(" ")

favSeason = input('What is your favorite season? ')

if(favSeason == 'Fall'):

print("Wow! That is my favorite season also! The colors of the leaves are amazing")

print(" ")

else:

print("Nice! My favorite season is Fall!")

print(" ")

siblings = input('Do you have any siblings in your family? ')

if(siblings == 'Yes'):

print("Very nice, back when I was born a human I grew up with a sister")

print(" ")

else:

print("An only child I see")

print(" ")

stateBorn = input('What state were you born in? ')

if(stateBorn == 'West Virginia'):

print("My creator is also from there!")

print(" ")

else:

print("What a lovely state")

print(" ")

#end questions

print("Well I thank you for your time but that is all the time we have, thank you for joining me today")

You have been hired by the Coca-Cola Company to determine if students at Oregon State University prefer Coke or Pepsi. A taste test was performed where students were given two identical cups and were asked to taste both drinks. They had to report which drink they prefer. It was found that 69 out of 125 students indicated they preferred cup that contained Coke.

1. (4 pts) What is the random variable in this problem? Does the random variable have a binomial distribution? Explain. (Recall, there are 4 checks for a discrete random variable to have a binomial distribution – make sure you list all 4. Discuss in detail if you think the “observations are independent of each other”.)

2. (1 pt) What does ?? represent in the context of this study?

3. (1 pt) Calculate the sample proportion, ??̂, of students in the sample prefer Coke. Show work.

4. Perform a hypothesis test to determine if OSU students prefer one brand over the other by answering the following questions:

a. (3 pts) State the null and alternative hypotheses in statistical notation. Define any notation used. (Hint: if there really is no preference, would be expect 50% to prefer Coke and 50% to prefer Pepsi?)

b. (3 pts) Report the p-value and state a conclusion in a complete sentence in the context of the problem.

c. (3 pts) Report a 95% confidence interval for the proportion of all OSU students who prefer Coke. Interpret this confidence interval in the context of the problem.

5. (2 pts) Do you believe it is legitimate to use the results of this hypothesis test and confidence interval to make a conclusion about all OSU students? Why or why not?