Student Debt – Vermont: You take a random sample of 31 college students in the state of Vermont and find the mean debt is $25,000 with a standard deviation of $2,700. We want to construct a 90% confidence interval for the mean debt for all Vermont college students.

(a) What is the point estimate for the mean debt of all Vermont college students?
$
(b) What is the critical value of t for a 90% confidence interval? Use the value from the t-table.

(c) What is the margin of error for a 90% confidence interval? Round your answer to the nearest whole dollar.
$
(d) Construct the 90% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar.
(  ,  )

(e) Interpret the confidence interval.

A We expect that 90% of all Vermont college students have a debt that's in the interval.

B We are 90% confident that the mean student debt of all Vermont college students is in the interval.

C We are confident that 90% of all Vermont college students have a debt that's in the interval.

D We are 10% confident that the mean student debt of Vermont college students is in the interval.

(f) We are never told whether or not the parent population is normally distributed. Why could we use the above method to find the confidence interval?

A Because the sample size is greater than or equal to 30.Because the sample size is greater than or equal to 15.   

B Because the margin of error is positive.Because the margin of error is less than or equal 30.

C Because the margin of error is positive.

D Because the margin of error is less than or equal 30.

A local car dealer closes on Sundays at 6:00 pm. He counts the number

of cars available at that time. If there are two or less, order enough to

raise the level to six. Cars are delivered at night and are available when

the exhibition hall opens at 9:00 a.m. on Monday morning. Let Pd (x) be

the probability that the demand during the week is equal to x: Suppose that:

Pd (0) = 0.2 ,Pd (1) = 0.5 ,Pd (2) = 0.2 ,Pd (3) = 0.1

If there is more demand than cars during the week than those available at the

start of it, the excess demand is wasted and the distributor ends the week with

zero cars available. Define a markov chain where states are numbers of cars

available on Monday morning at 9:00 am. Find the transition matrix.

A simple random sample of size n is drawn. The sample​ mean, x ​, is found to be 19.5​, and the sample standard​ deviation, s, is found to be 4.6.

a) Construct a 95% Confidence interval about μ if the sample size n, is 35

(Use ascending order to round to two decimal places as needed

lower bound= Upper bound=

b) Construct a 95% Confidence interval about μ if the sample size n, is 61

lower bound= Upper bound =

(a). How does increasing the level of confidence affect the size of the margin of​ error, E?

A.The margin of error increases.

B.The margin of error decreases.

C.The margin of error does not change

d) If the sample size is

Construct a 99% Confidence interval about μ if the sample size n, is 35

lower bound= Upper bound =

Compare the results to those obtained in part​ (a). How does increasing the level of confidence affect the size of the margin of​ error, E?

A. The margin of error increases.

B.The margin of error decreases.

C.The margin of error does not change.

3. If the sample size is 18 what conditions must be satisfied to compute the confidence​ interval?

A.The sample size must be large and the sample should not have any outliers.

B.The sample data must come from a population that is normally distributed with no outliers.

C.The sample must come from a population that is normally distributed and the sample size must be large.

A class has 40 students.

Thirty students are prepared for the exam, • Ten students are unprepared.

The professor writes an exam with 10 questions, some are hard and some are easy.

• 7 questions are easy. Based on past experience, the professor knows that:

– Prepared students have a 90% chance of answering easy questions correctly

– Unprepared students have a 50% chance of answering easy questions correctly.

• 3 questions are hard. Based on past experience, the professor knows that:

– Prepared students have a 50% chance of answering hard questions correctly

– Unprepared students have a 10% chance of answering hard questions correctly

• Each student’s performance on each question is independent of their performance on other questions.

(a) Find the probability that a prepared student answers all 10 questions correctly.

(b) What is the probability that at least one of the 30 prepared students answers all 10 questions correctly. Assume that each student’s score is independent of every other student.

(c) Let P be the number of questions answered correctly by a randomly chosen prepared student, and let U be the number answered correctly by a randomly chosen unprepared student. Find E[P] and E[U]

a simple random sample of 225 college students was taken in order to estimate the proportion of college students that agrees with the "no teacher left alone act". of those surveyed, 142 agreed with the law. construct the 95% confidence interval estimate of the proportion of all college students that agrees with this law

Sample
80
80
80
81
81
64
65
65
66
67
67
67
71
71
72
72
72
72
73
73
73
90
91
93
96

Today, the professor claims the mean student performance on his midterm has significantly improved from last year. Last year, the mean midterm score for all of his students was 70. The professor uses a random sample of 25 student’s midterm scores (column 2). Use a hypothesis test (t-test) to test the professors claim using a 5% significance level.

1) What is the value of the test statistic?

2) What is the critical value from the t-table?

3) What is the p-value?

4) Can the professor conclude this year’s mean midterm score has improved? Explain!

While regression analysis is a useful tool for making budgeting predictions, learning how to become proficient in regression analysis is beyond the scope. But, knowing what regression analysis can do for the budgeting process is important. Write a short paragraph, or two, explaining what you feel regression analysis can provide during the budgeting process.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 60 professional actors, it was found that 35 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)


(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 95% confident that the true proportion of all actors who are extroverts falls outside of 0.46 and 0.71.We are 5% confident that the true proportion of all actors who are extroverts falls between 0.46 and 0.71.    We are 5% confident that the true proportion of all actors who are extroverts falls above 0.46 and 0.71.We are 95% confident that the proportion of all actors who are extroverts falls between 0.46 and 0.71.

(c) Do you think the conditions np is greater than or equal to 15 and n*(1 - p) is greater than or euqal to 15 are satisfied in this problem? Explain why this would be an important consideration.

A No, the conditions are not satisfied. This is important because it allows us to say that the sampling distribution of p̂ is approximately normal.

B Yes, the conditions are satisfied. This is important because it allows us to say that the sampling distribution of p̂ is approximately binomial.

C No, the conditions are not satisfied. This is important because it allows us to say that the sampling distribution of p̂ is skewed right.

D Yes, the conditions are satisfied. This is important because it allows us to say that the sampling distribution of p̂ is approximately normal.

Let A,B, and C be independent random variables, uniformly distributed over [0,9] [0,6],and [0,8] respectively. What is the probability that both roots of the equation Ax2+Bx+C=0are real?

please answer all parts of question, thank you so much

12. Identify the correct statements. Fix the incorrect ones.

a. A sampling distribution describes the distribution of data values.

b. A sampling distribution shows the behavior of a sampling process over many samples.

c. The probability distribution of a parameter is called a sampling distribution.

d. Sampling distributions describe the values of a data summary for many samples.

14. 14. Why is random sampling important?

18. A large university wants to send an exit survey to a SRS of 500 of its 3,827 graduating seniors. One question is, “Would you recommend to others that they should attend the university?” The response choices are: not sure, not likely, likely, definitely, most definitely. Describe how you would (in theory) use repeated sampling to obtain the sampling distribution of the sample proportion who would “definitely” or “most definitely” recommend the university to others.

It is generally accepted that patients grow anxious when a person with a white coat and stethoscope walks into an examining room; i.e., patients have white coat hypertension. A family practitioner hypothesizes the opposite effect. To test this, the practitioner has colleagues from the practice randomly visit patients in a white coat or non-white sport coat, and measure their blood pressure. What can the practitioner conclude with an α of 0.05? Below are the systolic blood pressures of the patients.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Condition 1:
---Select--- examining room white coat hypertension non-white coat white coat blood pressure
Condition 2:
---Select--- examining room white coat hypertension non-white coat white coat blood pressure

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

d) compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

e) Make an interpretation based on the results.

The systolic blood pressure for patients that where visited by a practitioner with a white coat was significantly higher from patients that were visited by a practitioner in a non-white sport coat.

The systolic blood pressure for patients that where visited by a practitioner with a white coat was significantly lower from patients that were visited by a practitioner in a non-white sport coat.    

The systolic blood pressure for patients that where visited by a practitioner with a white coat did not significantly differ from patients that were visited by a practitioner in a non-white sport coat.

1. Suppose it is claimed that the mean weight of a bag of the same brand of candies is 0.13 ounces. You wish to show that it is not 0.13 ounces and wish to test the claim at α = 0.01 level. You collected a sample of 16 small bags of the same brand of candies. The weight of each bag was then recorded. The mean weight was two ounces with a standard deviation of 0.12 ounces. Assume that the population distribution of bag weights is normal with a known population standard deviation of 0.1 ounce.
   1. State the null and alternate hypotheses clearly.
   2. Conduct the hypothesis test based on the test statistic and critical value(s). Clearly indicate each.
   3. What is the p-value? Use the p-value to conduct the same test
   4. Report your conclusion in words, in the context of the problem.

*Work on excel*

1. You’ve been assigned to a special quality control task force in your firm to assess the performance reliability of your firm’s three regional factories (Factory A, Factory B, and Factory C) where desk lamps are manufactured.

Your task force collected the following background information (where A = Factory A; B = Factory B,
C = Factory C, D = defective).

If a randomly selected lamp is defective,

            a. What is the probability that the lamp was manufactured in Factory A?

            b. What is the probability that the lamp was manufactured in Factory B?

            c. What is the probability that the lamp was manufactured in Factory C?

A software engineer is creating a new computer software program. She wants to make sure that the crash rate is extremely low so that users would give high satisfaction ratings. In a sample of 780 users, 39 of them had their computers crash during the 1-week trial period.

(a)

What is the sample size?

What is p̂?

(b)

What is the 95% confidence interval for p̂? (Use a table or technology. Round your answers to three decimal places.)