You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 54% at a level of significance of αα = 0.01. According to your sample, 38 out of 61 potential voters prefer the Democratic candidate.

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:
   Ho: ? p μ  ? = ≠ < >   (please enter a decimal)   
   H₁: ? p μ  ? = > < ≠   (Please enter a decimal)

3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer reject accept fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly larger than 54% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 54%.
   • The data suggest the populaton proportion is significantly larger than 54% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 54%
   • The data suggest the population proportion is not significantly larger than 54% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 54%.
8. Interpret the p-value in the context of the study.
   • There is a 9.68% chance that more than 54% of all voters prefer the Democratic candidate.
   • If the sample proportion of voters who prefer the Democratic candidate is 62% and if another 61 voters are surveyed then there would be a 9.68% chance of concluding that more than 54% of all voters surveyed prefer the Democratic candidate.
   • There is a 9.68% chance of a Type I error.
   • If the population proportion of voters who prefer the Democratic candidate is 54% and if another 61 voters are surveyed then there would be a 9.68% chance that more than 62% of the 61 voters surveyed prefer the Democratic candidate.
9. Interpret the level of significance in the context of the study.
   • If the proportion of voters who prefer the Democratic candidate is larger than 54% and if another 61 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 54%.
   • If the population proportion of voters who prefer the Democratic candidate is 54% and if another 61 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is larger than 54%
   • There is a 1% chance that the earth is flat and we never actually sent a man to the moon.
   • There is a 1% chance that the proportion of voters who prefer the Democratic candidate is larger than 54%.

In an introductory statistics class, there are 18 male and 22 female students. Two students are randomly selected (without replacement).

(a) Find the probability that the first is female

(b) Find the probability that the first is female and the second is male.

(c) Find the probability that at least one is female

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I know that this question has to use the counting method, but i got confuse with how to start because i have to now find the probability of FIRST being a female, etc. Please provide workings with explanations alongside. Thank you in advance!

A scatterplot is the best way to show the mode of a categorical variable. (True/False)

An observational study with a convenience sample provides the strongest evidence that a predictor causes an outcome. (True/False)

Given a normal distribution, find the percentage of observed records that will be within 1.5 standard deviations (1.5 standard deviation to the left AND right of the mean). Show calculations and/or R code used to find your answer.

1. A composites manufacturer is having serious problems with porosity in their parts. A Quality Engineer samples 300 parts and finds 58 defective.

1. Test the hypothesis that defective rate (proportion defective) exceeds 15%. Test at a = 0.05.

What is the parameter of interest?   What assumptions are made? Show mathematical evidence to support assumption.

i. Write the null and alternative hypotheses.

ii. Calculate the test statistic.

iii. Determine the reject region. Find the p-value. Show normal graph including reject region and test statistic.

iv. Make a decision and write a thorough interpretation in context of the problem.

v. If in reality the true proportion defective is 12%, what type of error, if any, occurred?

2. Compute the power of the test if the true defective rate is 0.18.
3. Suppose that you wanted to reject the null hypothesis with probability at least 0.9 if true defective rate p = .18. What sample size should be used?
4. Construct a 95% Confidence Interval for p, the true proportion defective.

( PLEASE SHOW ALL YOUR WORK). I

MPORTANT NOTE: Make sure you do the following: -State Ho and Ha using notation for each hypothesis test conducted. -Use α= 0.05 for all hypothesis tests conducted. -Explain all results obtained for both hypothesis tests and confidence intervals.

You will need your ticker code (company abbreviation) for stock prices for this question. Use your ticker code to obtain the closing prices for the following two time periods to obtain two data sets:

March 2, 2019 to March 16, 2019

Data set A

February 16, 2019 to February 28, 2019

Data set B

Take the closing prices from data set B and add 0.5 to each one of them. Treat data sets A and B as hypothetical sample level data on the weights of newborns whose parents smoke cigarettes (data set A), and those whose parents do not (data set B).

a) Conduct a hypothesis test to compare the variances between the two data sets.

b) Conduct a hypothesis to compare the means between the two data sets. Selecting the assumption of equal variance or unequal variance for the calculations should be based on the results of the previous test.

c) Calculate a 95% confidence interval for the difference between means

A school psychologist believes that a popular new hypnosis technique increases depression. The psychologist collects a sample of 25 students and gives them the hypnosis once a week for two months. Afterwards the students fill out a depression inventory in which their average score was 53.88. Normal individuals in the population have a depression inventory average of 50 with a variance of 100.00. What can the psychologist conclude with α = 0.01?

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

b)
Population:
---Select--- students receiving hypnosis ,normal individuals, two months ,new hypnosis ,technique depression
Sample:
---Select--- students receiving hypnosis ,normal individuals ,two months, new hypnosis ,technique depression

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.)
critical value = ; test statistic =  
Decision: ---Select--- Reject H0 or Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[ , ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and 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

f) Make an interpretation based on the results.

A.The depression of students that underwent hypnosis is significantly higher than the population.

B.The depression of students that underwent hypnosis is significantly lower than the population.    

C.The depression of students that underwent hypnosis is not significantly different than the population.

True or False

1. T F   Six Sigma relates to a 3.4 DPMO.

2. T F Six Sigma can not be applied to service companies.

3. T F   Walter Shewhart stated that, “A phenomenon is said to be in statistical control when, through the use of past experience, we can say that our product is within the specification limits.”

4. T F   Variation exists in every process.

5. T F   Potential sources of variation include methods, manpower, material, and equipment.

6. T F   The voice of the customer is usually expressed on the control chart as control limits.

7. T F   Quality begins with control and inspection.

8. T F   Product quality is determined during the manufacturing of the product.

9. T F   Most companies operate at a 3 to 4 sigma level.

10. T F   The project charter serves as contract between project team and sponsor.

11. T F   Once the project charter is develop and completed, it should not be changed in order to avoid confusion.

A genetic experiment involving peas yielded one sample of offspring consisting of 416 green peas and 144 yellow peas. Use a 0.05 significance level to test the claim that under the same circumstances, 23% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P value, conclusion about the null hypothesis, and the final conclusion that addresses the The original claim. Use the P value method and the normal distribution as an approximation to the binomial distribution.

1. One of the most important measures of the quality of service provided by any firm is the speed with which it responds to customer complaints. Comcast, a U.S. global telecommunications conglomerate, wants to greatly improve its customer satisfaction. Comcast states the desired mean call time involving customer complaints is 12 minutes (including wait time). Assume the standard deviation is known to be 0.15 minutes. A sample of 70 customer calls yields a mean time of 12.14 minutes. This sample will be used to obtain a 99% confidence interval for the mean time of a customer complaint call. Round final answers to two decimal places. Solutions only.

(A) The critical value to use in obtaining the confidence interval is.

(B) The confidence interval goes from to.

(C) True, False, or Uncertain: The confidence interval indicates that Comcast is not meeting its goal.

(D) True, False, or Uncertain: The confidence interval is valid only if the length of calls are normally distributed

(E) Suppose the manager had decided to estimate the mean call time to within 0.03 minutes with 99% confidence. Then the sample size would be?

Ada Nixon, a student, has just begun a 30-question, multiple-choice exam. For each question, there is exactly one correct answer out of four possible choices. Unfortunately, Ada hasn't prepared well for this exam and has decided to randomly select an answer choice for each question.

(a) (4 points) For a given question, what is the probability Ada picks the correct answer, assuming each answer choice is equally likely to be selected?

(b) Assume the number of questions Ada answers correctly is Binomially distributed.

i. (4 points) What is the average number of questions Ada will answer correctly? Show your work and round your nal answer to 1 decimal place.

ii. (3 points) If Ada answers at least 16 questions correctly, she will receive a passing grade. What is the probability that Ada receives a passing grade? Show your work, including any calculator functions you use, and round your nal answer to 3 decimal places.

(c) (3 points) Suppose Ada comes across a question for which she knows two of the answer choices are certainly wrong, which means the correct answer must be one of the two remaining choices. Assuming Ada will answer every other question using the same random selection procedure as before, will the number of questions she answers correctly remain binomially distributed? State Yes or No and explain why

A random sample is drawn from a normally distributed population with mean μ = 19 and standard deviation σ = 1.8. [You may find it useful to reference the z table.]

a. Are the sampling distribution of the sample mean with n = 27 and n = 54 normally distributed?

Yes, both the sample means will have a normal distribution.

No, both the sample means will not have a normal distribution.

No, only the sample mean with n = 27 will have a normal distribution.

No, only the sample mean with n = 54 will have a normal distribution.

b. Calculate the probabilities that the sample mean is less than 19.9 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

A fun size bag of M&Ms has 4 blue, 3 orange, 3 red, 2 green, 2 yellow, and 1 brown M&Ms. What is the probability of randomly selecting 5 M&Ms where 3 are blue and 2 are orange?

Flair Furniture Company produces inexpensive tables and chairs. The production process for each is similar in that both require a certain number of labor hours in the carpentry department and a certain number of labor hours in the painting department. Each table takes 3 hours of carpentry work, an hour and a half of assembly and 2 hours of finishing work. Each chair requires 4 hours of carpentry, and hour and 15 minutes of assembly and 1 hour of painting. During the current month, 2,400 hours of carpentry time, 800 hours of assembly time and 1,000 hours of painting time are available. Each table sold results in a profit contribution of $7, and each chair sold yields a profit contribution of $5.

a. Set up a Solver model for determine the number of tables and chairs to produce that will maximize total profit contribution. Run Solver and generate the Answer Report and Sensitivity Report.

b. Identify the binding and nonbinding constraints and explain what it means.

c. Construct the sensitivity range for the objective function coefficients. Give an interpretation for each range.

d. Construct the sensitivity range for the right hand side coefficient of constraints. Give an interpretation for each range and the corresponding shadow price of all the constraints.

e. Suppose that 100 hours of additional labor can be added. In which department would you add these hours? Explain why. How much additional profit can be generated by this addition?

3) A tax auditor has a pile of federal tax returns and she has been directed to randomly select 20 of these returns for a special audit. Describe how systematic sampling could be used. 4) A recent radio station asked listeners to go to their website and vote for their favorite singing star. A responder would be randomly chosen and would receive two tickets to the performance of their choice. What type of sampling is used for the vote? 5) A community college is selected at random from all US community colleges and the GPAs and ages of all students from that college are examined. a) What type of sampling was done? b) What is the population of interest for this study? c) If the average GPA is computed for this sample would it be considered a statistic or a parameter? d) Suppose instead the researchers wanted to implement a Simple Random Sample of community college students, how might they do this? 6) Explain the difference between cluster sampling and stratified sampling.