A steel company is considering the relocation of one of its manufacturing plants. The company’s executives have selected four areas that they believe are suitable locations. However, they want to determine if the average wages are significantly different in any of the locations, since this could have a major impact on the cost of production. A survey of hourly wages of similar workers in each of the four areas I performed with the following results.

a. Do the data indicate a significant difference among the average hourly wages in the four areas? Construct the 10 steps of hypothesis testing using α = 0.05 to answer the question.

b. What assumptions were mad in performing the test in part a? Do the data appear to satisfy these assumptions? Explain.

Problem 2: (Revised 6.3) Magazine Advertising: In a study of revenue from advertising, data were collected for 41 magazines list as follows. The variables observed are number of pages of advertising and advertising revenue. The names of the magazines are listed as:

Here is the code help you to paste data into your R:

data6<-'Adv Revenue
25 50
15 49.7
20 34
17 30.7
23 27
17 26.3
14 24.6
22 16.9
12 16.7
15 14.6
8 13.8
7 13.2
9 13.1
12 10.6
1 8.8
6 8.7
12 8.5
9 8.3
7 8.2
9 8.2
7 7.3
1 7
77 6.6
13 6.2
5 5.8
7 5.1
13 4.1
4 3.9
6 3.9
3 3.5
6 3.3
4 3
3 2.5
3 2.3
5 2.3
4 1.8
4 1.5
3 1.3
3 1.3
4 1
2 0.3
'
data6n<-read.table(textConnection(object=data6),
header=TRUE,
sep="",
stringsAsFactors = FALSE)

a. You should not be surprised by the presence of a large number of outliers because the magazines are highly heterogeneous and it is unrealistic to expect a single relationship to connect all of them. Find outliers and high leverage points. Delete the outliers and obtain an acceptable regression equation that relates advertising revenue to advertising pages.

b. For the deleted data, check the homogeneity of the variance. Choose an appropriate transformation of the data and fit the model to the transformed data. Evaluate the fit.

Use R.  Provide Solution and R Code within each problem.

A study was conducted to determine the average weight of newborn babies. The distribution of the weight of newborn babies has a standard deviation of σ = 1.25lbs. A random sample of 100 newborn babies was taken and weights measured. The mean weight of the babies in the sample was 7.3 lbs.

a. Construct a 95% confidence interval for the true mean weight of newborn babies.

b. Interpret the confidence interval in a.

c. Write the null and alternative hypotheses to determine if the true mean weight of newborn babies is less than 7.75 lbs.

d. Conduct a statistical test to determine if the true mean weight of newborn babies is less than 7.75 lbs.

i. Pvalue

ii. Conclusion

> fm1 <- lm(ascorbic ~ pct.dry + cultB.id + cultC.id, data=lima)

> summary(fm1)

Coefficients: Estimate Std. Error t value Pr(>|t|)

(Intercept) 213.2 16.3 13.1 4.64e-08 ***

pct.dry    -3.9 0.43 -9.1 1.96e-06 ***

cultB.id -6.2 5.53 -1.1 0.290

cultC.id    20.5 5.42 3.8 0.003 **

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

Residual standard error: -- intentionally omitted -Multiple R-squared: 0.91, Adjusted R-squared: 0.88 F-statistic: 36.84 on 3 and 11 DF, p-value: 4.956e-06

(c) Determine whether each of the statements below is supported by the multiple regression model above. If the statement is supported, circle “yes”. If the statement is not supported, circle “no”.
YES NO (i) After controlling for differences among the cultivars, there is strong evidence that ascorbic acid content decreases as percent dry weight increases.
YES NO (ii) The estimate of the intercept suggests that lima bean plans of cultivar A have an average ascorbic acid content of 213.
YES NO (iii) After accounting for the effect of percent dry weight, there is strong evidence that the ascorbic acid content of cultivar B is less than the ascorbic acid content of cultivar A.
YES NO (iv) After accounting for the effect of percent dry weight, there is strong evidence that the ascorbic acid content of cultivar C is less than the ascorbic acid content of cultivar A.

The drive-thru times at Tim Horton’s are normally distributed with µ = 138.5 seconds and σ = 29 seconds.

(a) What is the probability that a randomly selected car will get through the drive-thru in less than 100 seconds?

(b) What is the probability that a randomly selected car will spend more than 160 seconds in the drive-thru?

(c) What proportion of cars spend between 2 and 3 minutes in the drive-thru?

(d) Would it be unusual for a car to spend more than 3 minutes in the drive-thru? Why?

The City of Charlotte is experiencing flooding. The City has determined that it will activate the flood

gates when the average flood level reaches 2 feet. The flood control system is activated and

resources are directed to flood control when the flood condition is equal to or more than the 2 feet

standard the City has set. The City sampled 20 spots in the urban area between 7:00am and 8:00am.

This data set will be posted to Canvas. Examine the data using the concepts you have learned in

Chapter 10. Should the City activate the flood control system? Why or why not?

Data Set:

Areas. Feet of Flood Water

1 0

2 3

3 1

4 2

5 0

6 0

7 2

8 3

9 1

10 3

11 2

12 2

13 5

14 1

15 2

16 0

17 2

18 1

19 0

20 2

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?