Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally distributed. You randomly catch and weigh 17 such salmon. The mean weight from your sample is 22.2 pounds with a standard deviation of 4.4 pounds. You want to construct a 95% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River.

(a) What is the point estimate for the mean weight of all spawning Chinook salmon in the Columbia River?
pounds

(b) Construct the 95% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River. Round your answers to 1 decimal place.
< μ <   

(c) Are you 95% confident that the mean weight of all spawning Chinook salmon in the Columbia River is greater than 18 pounds and why?

No, because 18 is above the lower limit of the confidence interval.Yes, because 18 is below the lower limit of the confidence interval.     No, because 18 is below the lower limit of the confidence interval.Yes, because 18 is above the lower limit of the confidence interval.

(d) Recognizing the sample size is less than 30, why could we use the above method to find the confidence interval?

Because the parent population is assumed to be normally distributed.Because the sample size is greater than 10.     Because we do not know the distribution of the parent population.Because the sample size is less than 100.

Pro-choice/Pro-life and Region of the Country: The results of a 2013 Gallup poll about people's position on abortion (pro-life or pro-choice) by region of the country are summarized in the contingency table below.

Observed Frequencies: O_i's

The Test: Test whether or not there is a dependent relationship between abortion stance and region. Conduct this test at the 0.05 significance level.

(a) What is the test statistic? Round your answer to 3 decimal places.

χ²

=  

(b) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀     

(c) Choose the appropriate concluding statement.

We have proven abortion stance and region are independent. The evidence suggests that there is a dependent relationship between abortion stance and region.       There is not enough evidence to conclude that there is a dependent relationship between abortion stance and region.

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.82.

(a) Use the Normal approximation to find the probability that Jodi scores 77% or lower on a 100-question test. (Round your answer to four decimal places.)


(b) If the test contains 250 questions, what is the probability that Jodi will score 77% or lower? (Use the normal approximation. Round your answer to four decimal places.)


(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?
questions

(d) Laura is a weaker student for whom p = 0.77. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also?

Yes, the smaller p for Laura has no effect on the relationship between the number of questions and the standard deviation.No, the smaller p for Laura alters the relationship between the number of questions and the standard deviation

Exam 1

1- Let a Population be { 5,7,9,11,13,15}

Find the sample mean distribution for pairs.

(a)Find the Mean + Standard deviation of your distribution

(2)Sketch The distribution.

(3)Compare the values of the mean and standard deviation of the probability mean distribution and the population.

“ Do not give decimals , give exact values”

Extra credit : Do problem #1 using R

10.33- In each of the following examples,state whether we are sampling from a finite population or a hypothetically infinite population , and describe the population.

a-A personnel manager selects 5 of 20 job applicants for an interview.

b-We weigh a gold nugget three times and use the average we obtain as its weight.

c-We observe how many heads we get in 100 flips of a balanced coin.

d-We select 5 of 25 picture postcards displayed in a store to mail to friends.

e-We observe the gasoline mileage obtained by our car for a period of time estimate the miles per gallon for the car.

10.34- Obtain the probability , by counting , of each possible sample if a random sample of size 2 is taken from

a-A finite population of size 3.

b-A finite population of size 4.

10.35- When we sample from an infinite population , what happens to the standard error of the mean when the sample size is

a-Increased from 30 to 120.

b-Decreased from 245 to 5.

10.36- When we sample from an infinite population , what happens to the standard error of the mean when the sample size is

a-Decreased from 1000 to 10?

b-Increased from 80 to 500

10.37- What is the value of the finite population correction factor when

1-N= 100 and n= 10;

2-N=300 and n=25

3-N=5000 and n=100

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level.

Step 2 of 2 :  

Suppose a sample of 801 tenth graders is drawn. Of the students sampled, 577 read above the eighth grade level. Using the data, construct the 95%confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.

The data show the list and selling prices for several expensive homes. Find the regression​ equation, letting the the list price be the independent​ (x) variable. Find the best predicted selling price of a home having a list price of ​$2 million. Is the result close to the actual selling price of $1.7 ​million? Use a significance level of 0.05.

List price__Selling price
4.4_____4.7
2.1_____1.7
4.5______4
3.4______3
1.9_____1.7
2.2_____1.7

A student studying for a vocabulary test knows the meanings of 10 words from a list of 26 words. If the test contains 10 words from the study list, what is the probability that at least 8 of the words on the test are words that the student knows? (Round your answer to three decimal places.)

James Short was a maker of optical instruments, particularly telescopes. He was born in Edinburgh, Scotland and entered the University of Edinburgh in 1726, where he attended lectures by the mathematician Colin Maclaurin. Short is perhaps best remembered for his observations of the transit of Venus on June 6, 1761. His profession made him quite a rich man, by the way. The attached table (see the txt file) provides James Short's measurements of the parallax of the sun (in seconds of a degree), based on the 1761 transit of Venus. There were two samples of observations collected (under two different conditions). The total number of cases is 53 and the "true" value is 8.798. The parallax of the sun is the angle subtended by the earth, as seen from the surface of the sun.

a) Construct the 95% confidence interval for μ based on the combined sample. Is the true value of the parallax of the sun in this interval?

b) Construct the 95% confidence interval for σ based on the combined sample.

c) Test a hypothesis that the parallax of the sun differs from 9 seconds of a degree, based on the combined sample at the 0.1 significance level.

d) For two samples, verify if the true means of the populations they are taken from differ insignificantly at the 0.05 significance level.

e) For two samples, verify if the ratio of the true variances of the populations they are taken from differ insignificantly at the 0.05 significance level.

f) Write a short summary of your analysis. Show your work. Write clearly all assumptions.

txt file is below,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Parallax

Sample 1
8.5
8.5
7.33
8.64
9.27
9.06
9.25
9.09
8.5
8.06
8.43
8.44
8.14
7.68
10.34
8.07

Sample 2
8.36
9.71
8.65
8.35
8.71
8.31
8.36
8.58
7.8
7.71
8.3
9.71
8.5
8.28
9.87
8.86
5.76
8.44
8.23
8.5
8.8
8.4
8.82
9.02
10.57
9.11
8.66
8.34
8.6
7.99
8.58
8.34
9.64
8.34
8.55
9.54
9.07

(1) Suppose that the mean effect during a flight of an anti-stall mechanism in a plane is a height change of 0 meters with a standard deviation of 1 meter, and the effects have a normal distribution. If planes fly 1000 flights with this anti-stall mechanism, what is the expected value (or mean value) of the number of flights in which the effect during the flight of the anti-stall mechanism would be classified as an outlier, according to the 1.5 IQR criterion? Write your answer as a decimal accurate to two decimal places.

Research is an integral part of all professional fields. Designing a research study can be a complicated task that can be simplified if the appropriate techniques can be identified. This assignment will give you the opportunity to design an experiment, including finding relevant prior research, determining the appropriate sample, data analysis techniques, and discuss the results you hope to see. Working from the topic chosen earlier in the topic selection, you will be designing your own statistical study. In a 1,250-1,500 word report, discuss the design of an experiment that would expand on or relate to the research in the previously chosen article. See the attached document for detailed instructions on how to complete the project. A minimum of four additional scholarly resources are required. **Research must be on "Physician Burnout"**

MAT-274 Final Project Detailed Criteria
Background information explaining the importance of the research (why it should be done) and what has been done in the past.
- This background section can be a large portion of your paper, perhaps around 25% of the entire word count. Here you explain what previous research has been done on your topic and how this inspired your new study/experiment. You are required to reference four scholarly articles in your final paper. Make sure to mention how the study you designed is different from the previous work you read in your primary research articles. You can also include information in this section about why the topic is important to your field of study or relevant to you in general.

Sampling and experimental design with rationale.
- In this section, you should include your sampling technique, how you are achieving appropriate randomization, and why this technique is the most appropriate for your particular experiment. Make sure you address any possible bias in your sampling technique and how you will consider this in your final results. Conclude this section with a discussion of your population for generalization and how the demographics of your sample achieve this goal.

Data analysis techniques (specific inferential test that would need to be used and why, include tests that would need to be done to validate the assumptions needed for the chosen inferential test).
- This section is the heart of your final paper. The final grading of the project will focus most heavily on this content. There are at least three paragraphs worth of material to comment on in this section. It is essential that you clearly articulate which type of inferential test you are using (z, t, paired t, pooled t, chi-squared, ANOVA+F-test, etc.). In addition to stating the type of test, you must explain why this test is appropriate. Every statistical test has certain conditions that must be satisfied to make the test have reasonable inferential power (see lecture slides on Loud Cloud). You need to verify that these assumptions are satisfied for your experiment/sample and explain what types of information you would collect to show this; mention any calculations, graphs, charts, and plots you would use. It would be very nice to include some information on how you would use Excel to implement these calculations/charts. The hypothesis test needs to be formally stated (null and alternative clearly and correctly given with variable names and inequalities/equalities in the correct spot). Describe whether this is a one-tailed or two-tailed test, your chosen significance level (with justification), and what the p-value would tell you in the context of your problem. If your test requires follow-up analysis (such as ANOVA, paired-t), you need to mention explicitly what type of follow up you will do and how these calculations would be performed. Why do you need the follow up calculations? What does this analysis tell you?

Expected results as well as the questions this research will serve to answer.
- This section can consist of a single paragraph and should discuss what exactly you hope to answer by performing your inferential test described in the previous part. State what results you expect to see for your hypothesis test, what do you expect the p-value to be approximately? What does the p-value tell you about your null/alternative? Would reject/fail to reject the null? Explain what your hypothesis test outcome means in language relevant to your chosen topic.

Suggestions for future research.
- Your paper should end with a concluding paragraph that discusses how your experiment might influence future research. Decide on future experiments that might be performed based off your work here and previous research. Outline any sample size/experimental design changes you would recommend to future researchers. How would this future research expand the work already completed?

A linguist is interested in knowing how best to learn a foreign language. The linguist develops a new way to learn a foreign language called Aural-Oral and wants to compare it to the traditional translation method. In a research study, students from a sample are randomly assigned to one of the methods: Aural-Oral, translation, and combination of both. In addition, the linguist wants to know if IQ is related to learning a foreign language, so the students are split into having a high or average IQ. After a year of studying a foreign language, the students are asked to take a vocabulary test on the foreign language. What can the linguist conclude with α = 0.05?

                              IQ

a) What is the appropriate test statistic?
---Select--- na One-Way ANOVA Within-Subjects ANOVA Two-Way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Method: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

IQ: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Mehotd: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
IQ: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is an IQ difference on vocabulary.There is no IQ difference on vocabulary.    

There is a method difference on vocabulary.There is no method difference on vocabulary.    

There is a method by IQ interaction on vocabulary.There is no method by IQ interaction on vocabulary.    

A telephone company claims that the service calls which they receive are equally distributed among the five working days of the week. A survey of 79 randomly selected service calls was conducted. Is there enough evidence to refute the telephone company's claim that the number of service calls does not change from day-to-day?

Step 1 of 10 : State the null and alternative hypothesis.

Step 2 of 10 : What does the null hypothesis indicate about the proportions of service calls received each day?

Step 3 of 10 : State the null and alternative hypothesis in terms of the expected proportions for each category.

Step 4 of 10 : Find the expected value for the number of service calls received on Monday. Round your answer to two decimal places.

Step 5 of 10 : Find the expected value for the number of service calls received on Thursday. Round your answer to two decimal places.

Step 6 of 10 : Find the value of the test statistic. Round your answer to three decimal places.

Step 7 of 10 : Find the degrees of freedom associated with the test statistic for this problem.

Step 8 of 10 : Find the critical value of the test at the 0.005 level of significance. Round your answer to three decimal places.

Step 9 of 10 : Make the decision to reject or fail to reject the null hypothesis at the 0.005

level of significance.

Step 10 of 10 : State the conclusion of the hypothesis test at the 0.005 level of significance.

Consider the following contingency table of observed frequencies. Complete parts a. through e. below.

Click the icon to view the contingency table.a. Identify the null and alternative hypotheses for a​ chi-square test of independence based on the information in the table. This test will have a significance level of

alphaαequals=0.100.10.

Choose the correct answer below.

A.

Upper H 0H0​:

The row and column variables are not independent of one another.

Upper H 1H1​:

The row and column variables are independent of one another.

B.

Upper H 0H0​:

The variables

Upper R 1R1​,

Upper R 2R2​,

Upper R 3R3​,

Upper C 1C1​,

Upper C 2C2​,

and

Upper C 3C3

are independent.

Upper H 1H1​:

At least one of the variables is not independent.

C.

Upper H 0H0​:

The variables

Upper R 1R1​,

Upper R 2R2​,

Upper R 3R3​,

Upper C 1C1​,

Upper C 2C2​,

and

Upper C 3C3

are independent.

Upper H 1H1​:

None of the variables are independent.

D.

Upper H 0H0​:

The row and column variables are independent of one another.

Upper H 1H1​:

The row and column variables are not independent of one another.

b. Calculate the expected frequencies for each cell in the contingency table.

c. Calculate the​ chi-square test statistic.

chi squaredχ2equals=nothing

​(Round to the two decimal places as​ needed.)d. Using

alphaαequals=0.100.10​,

determine the​ chi-square critical value

chi Subscript alpha Superscript 2χ2α

and state your conclusions.

chi Subscript alpha Superscript 2χ2αequals=nothing

​(Round to two decimal places as​ needed.)

State your conclusions.

The test statistic

chi squaredχ2

is

▼

less than

greater than

the critical value

chi Subscript alpha Superscript 2χ2α​,

so

▼

do not reject

reject

the

▼

alternative hypothesis.

null hypothesis.

There is

▼

insufficient

sufficient

evidence to indicate that

▼

none of the variables are independent.none of the variables are independent.

the row and column variables are not independent of one another.the row and column variables are not independent of one another.

the row and column variables are independent of one another.the row and column variables are independent of one another.

at least one of the variables is not independent.at least one of the variables is not independent.

the variables Upper R 1 comma Upper R 1 comma Upper C 1 comma Upper C 2 comma and Upper C 3 are independent.the variables R1, R1, C1, C2, and C3 are independent.

e. Determine the​ p-value using technology and interpret its meaning.

​p-valueequals=nothing

​(Round to three decimal places as​ needed.)

Interpret the meaning of the​ p-value.

The​ p-value is the probability of observing a

▼

critical value

test statistic

as extreme or more extreme than the one observed under the assumption that the

▼

alternative hypothesis

null hypothesis

is true. A​ p-value less than the significance level

alphaα

means that the

▼

critical value

test statistic

is

▼

unlikely

likely

enough that the

▼

alternative hypothesis

null hypothesis

should be rejected. For this​ test, the​ p-value is

▼

less than

greater than

alphaαequals=0.100.10​,

so

▼

do not reject

reject

the

▼

alternative hypothesis.

null hypothesis.

There is

▼

sufficient

insufficient

evidence to indicate that

▼

the row and column variables are not independent of one another.the row and column variables are not independent of one another.

none of the variables are independent.none of the variables are independent.

at least one of the variables is not independent.at least one of the variables is not independent.

the row and column variables are independent of one another.the row and column variables are independent of one another.

the variables Upper R 1 comma Upper R 1 comma Upper C 1 comma Upper C 2 comma and Upper C 3 are independent.the variables R1, R1, C1, C2, and C3 are independent.

Click to select your answer(s).

The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 in. A random sample of 25 rods has an average diameter of 0.5046 in.

(a) Test the hypothesis that mean rod diameter is 0.5025 in. Assume a two-sided alternative and use

(b) Find the P-value for this test.

(c) Construct a 95% two-sided confidence interval on the mean rod diameter.

he following data are for calculator sales in units at an electronics store over the past nine​ weeks:

Use trend projection with regression to forecast sales for weeks

10minus−13.

What are the error measures​ (CFE, MSE,

sigmaσ​,

​MAD, and​ MAPE) for this forecasting​ procedure? How about

r squaredr2​?

Obtain the trend projection with regression forecast for weeks

10minus−13.

​(Enter your responses rounded to two decimal​ places.)

Obtain the error measures.

CFE: MSE:   sigmaσ: MAD: MAPE:

Find the coefficient of determination (R squared)

R squared =