8. Suppose 22% of the eggs sold at a local grocery store that are graded “large” are smaller than that and should be graded “medium.” A random sample of 15 eggs graded large is obtained. Answer the following using the binomial distribution:(Round to 4 (FOUR) decimal places.)

What is the probability that 8 or more of the “large” eggs sampled are really medium-sized?

What is the probability fewer than 3 of the “large” eggs sampled are really medium-sized?

What is the probability that none of the “large” eggs sampled are really medium-sized?

What is the probability that exactly 4 of the “large” eggs sampled are really medium-sized?

What is the probability that all of the “large” eggs sampled are really medium-sized?

What is the probability that 6 or 7 of the “large” eggs sampled are really medium-sized?

The ages of commercial aircraft are normally distributed with a mean of 13.5 years and a standard deviation of 8.2933 years. What percentage of individual aircraft have ages between 10 years and 16 ​years? Assume that a random sample of 81 aircraft is selected and the mean age of the sample is computed. What percentage of sample means have ages between 10 years and 16 years?

The Perotti Pharma Company is investigating the relationship between advertising expenditures and the sales of some over-the-counter (OTC) drugs.

The following data represents a sample of 10 common OTC drugs. Note that AD = Advertising dollars in millions and S = Sales in millions $.

1. What is the equation of the regression line?

2. Interpret the slope in the context of the problem.

3. Find the coefficient of determination.

4. Interpret the meaning of R² in the context of the problem.

5. State the hypotheses to test for the significance of the regression equation.

6. Is there a significant relationship between dependent and independent variables at alpha=0.05? Why?

7. Create a 95% confidence interval for Sales if Advertising dollars = $50 million and interpret its meaning.

8. Paste the table with the results of regression analysis.

In one exit poll of n​ = 140​ voters, 66 said they voted for the Democratic candidate and 74 said they voted for the Republican candidate.

(a) Does a​ 95% confidence interval for the proportion voting for the Democratic candidate allow you to predict the​ winner? Why or why​ not?

​No, because some of the values in the interval are negative​ (less than​ 0) or greater than​ 1, depending on whether we define the proportion to be voting for the Republican or Democratic candidate.​No, because the interval includes a majority of people voting for the Democratic candidate and a majority of people voting for the Republican candidate.    Yes, because the interval includes a majority of people voting for the Democratic candidate and a majority of people voting for the Republican candidate​ (proportions both above and below​ 0.5).​Yes, because the interval ​doesn't include both values greater than 0.5 and values less than 0.5.​No, because the interval ​doesn't include values greater than 0.5​ (a majority of people voting for the Democratic​ candidate) and values less than 0.5​ (a majority of people voting for the Republican​ candidate). ​Yes, because all the values in the interval are positive​ (greater than​ 0) and less than 1.

(b) A​ 95% confidence interval with n​ = 1400 voters and counts 660 and 740 would give different results than those above. Explain why.

The larger sample size helps to reduce​ people's bias for one candidate or the other.The proportions of people who voted for the Democratic and Republican candidates would be different from those above.    The​ z-scores in the confidence intervals would be different for this confidence interval from those above.We have a larger margin of error when we have a larger sample​ size, giving us more precision to estimate the parameter. The larger sample size provides more​ information, so when I have the same amount of​ confidence, I have more precision to estimate the parameter.

State College is evaluation a new English composition course for freshmen. A random sample of n = 25 freshmen is obtained and the students are placed in the course during their first semester. One year later, a writing sample is obtained for each student and the writing samples are graded using a standardized evaluation technique. The average score for the sample is M = 76. For the general population of college students, writing scores form a normal distribution with a mean of µ > 70. a. If the writing scores for the population have a standard deviation of σ = 20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with α = .05. b. If the population standard deviation is σ = 10, is the sample sufficient to demonstrate a significant effect? Again, assume a two-tailed test with α = .05. c. Comparing your answers for parts a and b, explain how the magnitude of the standard deviation influences the outcome of a hypothesis test.

The null hypothesis states that the population mean is (answer with whole number).    With σ = 20, the sample mean corresponds to z = (round answer to two decimal places). This (is OR is not) sufficient to reject the null hypothesis. You (can OR cannot) conclude that the course has a significant effect. However if the population standard deviation is σ = 10, the sample mean corresponds to z = (round answer to two decimal places). This (is OR is not) sufficient to reject the null hypothesis and conclude that the course (does OR does not) have a significant effect.

Use your own words to describe the general steps necessary to answer a research question using biostatistics. Use an example to illustrate your described steps

Assignment Steps Resources: Microsoft Excel®, Signature Assignment Databases, Signature Assignment Options, Part 3: Inferential Statistics Scenario: Upon successful completion of the MBA program, say you work in the analytics department for a consulting company. Your assignment is to analyze one of the following databases: Manufacturing Hospital Consumer Food Financial Select one of the databases based on the information in the Signature Assignment Options. Provide a 1,600-word detailed, statistical report including the following: Explain the context of the case Provide a research foundation for the topic Present graphs Explain outliers Prepare calculations Conduct hypotheses tests Discuss inferences you have made from the results This assignment is broken down into four parts: Part 1 - Preliminary Analysis Part 2 - Examination of Descriptive Statistics Part 3 - Examination of Inferential Statistics Part 4 - Conclusion/Recommendations Part 1 - Preliminary Analysis (3-4 paragraphs) Generally, as a statistics consultant, you will be given a problem and data. At times, you may have to gather additional data. For this assignment, assume all the data is already gathered for you. State the objective: What are the questions you are trying to address? Describe the population in the study clearly and in sufficient detail: What is the sample? Discuss the types of data and variables: Are the data quantitative or qualitative? What are levels of measurement for the data? Part 2 - Descriptive Statistics (3-4 paragraphs) Examine the given data. Present the descriptive statistics (mean, median, mode, range, standard deviation, variance, CV, and five-number summary). Identify any outliers in the data. Present any graphs or charts you think are appropriate for the data. Note: Ideally, we want to assess the conditions of normality too. However, for the purpose of this exercise, assume data is drawn from normal populations. Part 3 - Inferential Statistics (2-3 paragraphs) Use the Part 3: Inferential Statistics document. Create (formulate) hypotheses Run formal hypothesis tests Make decisions. Your decisions should be stated in non-technical terms. Hint: A final conclusion saying "reject the null hypothesis" by itself without explanation is basically worthless to those who hired you. Similarly, stating the conclusion is false or rejected is not sufficient. Part 4 - Conclusion and Recommendations (1-2 paragraphs) Include the following: What are your conclusions? What do you infer from the statistical analysis? State the interpretations in non-technical terms. What information might lead to a different conclusion? Are there any variables missing? What additional information would be valuable to help draw a more certain conclusion?

There were 13 that landed on their bases.

4. Using your same data again from your 50 tosses, test the claim that the population proportion of Kisses® chocolates that land completely on the base is less than 35% at α = 5% level of significance. a. State the null and alternate hypotheses. Identify the claim. b. State the level of significance. c. Determine the standardized test statistic. (2 decimal places) d. Calculate the P-value. (4 decimal places) e. Make a decision to “reject the

5. Will your decision in problem #4 change if you test at α = 10% level of significance?

(All answers were generated using 1,000 trials and native Excel functionality.)

Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5,000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

1a)State two advantages of Bayesian data analysis over a classical approach?

1b)Explain why one would need a sensitivity analysis on the choice of prior distribution ?.

1. Objectives:

1) Select a simple random sample by random number table or Excel.

2) Know the sampling distribution of and, and calculate the probabilities by excel.

Q1: The director of personnel for Electronics Associates, Inc (EAI), has been assigned the task of developing a profile of the company’s 250 managers. The characteristics to be identified include the mean annual salary for the managers and the proportion of managers have completed the company’s management training program. Using the 2500 managers as the population for this study. (See data in a file named EAI).

Select a simple random sample of 30 managers from the 2500 EAI managers.

Q2: Business Weej conducted a survey of graduates from 30 top MBA programs (Business-Week, September 22, 2003). On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000, and for the female graduates, it is $25,000.

a. What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000?

b. What is the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000?

c. In which of the preceding two cases, part (a) and part (b), do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean? Comment on the results.

Q3: The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product’s label. Assume the population proportion p=0.76, and a sample of 400 consumers is selected from the population.

a. Show the sampling distribution of the sample proportion, where is the proportion of the sampled consumers who read the ingredients listed on a product’s label.

b. What is the probability that the sample proportion will be within +- 0.03 of the population proportion?

c. Answer part (b) for a sample of 750 consumers.

The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7.505 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 7.480 hours.

a. At the 0.05 level of significance, is there evidence that the mean life is different from 7.505 hours?

b. Compute the p-value and interpret its meaning.

c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.

d. Compare the results of (a) and (c). What conclusions do you reach?

In a group of 14 young professionals studied, it was found that they purchased on average $171.719 per month eating meals prepared outside the home, with a standard deviation of $36.011. What is the 90% confidence interval of the true amount of money young professionals spend monthly on meals prepared outside the home?

Question 3 options:

I'm a little confused regarding types of data & measurement scales for statistics, including: Nominal, Ordinal, Interval and Ratio.

If one were to categorize class standing, (1=freshmen, 2=sophomore, 3=junior and 4=Senior) would this be considered Nominal, Ordinal or interval? and why?

A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy until successful rehabilitation. Patient records in the rehabilitation center were examined, and 24 male subjects ranging in age from 18 to 30 years who had undergone similar corrective knee surgery during the past year were selected for the study. The number of days required for successful completion of physical therapy and the prior physical fitness status (below average, average, above average) for each patient follow.

1. Explore the with side-by-side box-plots. Discuss the results of your graphical exploration.
2. Calculate group mean and standard deviation.
3. Complete a one-way analysis of variance for this problem. Show all hypothesis-testing steps and interpret the results.