The Gallup-Healthways Well-being Index is a comprehensive survey of the health status of Americans.  A random sample of 2,580 adults were asked, "Have you ever been told by a physician or a nurse that you have depression?" Of these, 238 answered "Yes."

Using JMP construct the 99% confidence interval for the true proportion of Americans who have been told they have depression, and fill in the appropriate bounds in the confidence interval interpretation given below. Round your answers to two decimal places (i.e. 0._ _).

99% confident the true proportion of Americans who have been told by a physician or nurse they suffer from depression is between

and

Question 2 (1 point)

Refer to the scenario given in Question 1. According to the National Institute of Mental Health, 6.7% of adults suffer from depression. Is this percentage supported by the confidence interval found in Question1?

Question 2 options:

Question 3 (1.5 points)

Question 3 options:

A study investigated ways to prevent staph infection in surgery patients. In a first step, researchers examined the nasal secretions of a random sample of 6,771 patients admited to various hospitals for surgery. They found that 1,251 of these patients tested positive for Staphylococcus aureus, a bacterium responsible for most staph infections.

Using JMP, find the 90% confidence interval for the true prorportion of patients admitted for surgery that tested positive for Staphylococcus aureus, and fill in the apporpriate bounds in the confidence interval interpretation given below. Round your answers to two decimal places (i.e. 0._ _).

90% confident the true proportion of patients admitted for surgery that tested positive for Staphylococcus aureus is between

and

Question 4 (1 point)

Saved

Refer to the scenario given in Question 3. Suppose a hospital does not have to implement any measures to control for staph infections if the percentage of patients who test positive for Staphylococcus aureus is less than 18%. Based on the confidence interval constructed in Question 3, does the hospital have to worry about controlling for staph infections?

Question 4 options:

Provide two columns of data that are related and demonstrate the Excel Scatterplot Correlation and Regression methodology. Which is the Independent and Dependent variable?

2.51 Cards are drawn from a standard 52-card deck until an ace is drawn. After each card is drawn, it is put back in the deck and the cards are reshuffled so that each card drawn is independent of all others.

(a) Find the probability that the first ace is drawn on the 5th selection.

(b) Find the probability that at least 5 cards are drawn before the first ace appears.

(c) Repeat parts (a) and (b) if the cards are drawn without replacement. That is, after each card is drawn, the card is set aside and not replaced in the deck.

Purpose: To explore the sampling distribution for sample proportions.

Materials: One package of candies with multiple colors (M&M’s – any variety, Skittles – any variety, Reese’s Pieces, etc.). You may select any size package but be mindful of the “sample size” which will vary depending on the type of candy you choose. You may want to purchase at least a king size package to ensure you end up with a sample size that is “large enough.” Select a color whose proportion you are interested in exploring in the candy you have chosen.

I have chosen the following candy: M&M'S Milk Chocolate

I have selected the following color: Brown

Step 1: Identify your hypotheses. Do some internet research to identify what the company claims the proportion of your selected color to be for the candy you have chosen. Provide the link for the internet source you used. The proportion of M&M'S Milk Chocolate that are brown is 0.13 according to https://blogs.sas.com/content/iml/2017/02/20/proportion-of-colors-mandms.html

Calculate the proportion of your candies that are the color you have selected. The proportion of my sample of 250 M&M'S Milk Chocolate that are brown is 0.6.

Compare your sample proportion to the company’s claim. Do you think the true population proportion is different from the company’s claim? Write the null and alternative hypotheses you would use to investigate the answer to that question. Write them in symbolic notation AND write each hypothesis statement in a sentence.

Step 2: Check the conditions for normality. Check the conditions and assumptions necessary to use the normal model as an approximation for the sampling distribution you are exploring. Show your work and verify whether you have met the criteria necessary to proceed. (Hint: If your sample size is not large enough, increase your sample size!) Remember there are three conditions you need to check.

Step 3: Use your sample evidence to test your hypotheses. Make a sketch of your sampling distribution. Label the mean and standard deviation (SE), marking at least two SE in each direction. Mark your sample proportion in the sketch and shade appropriately. Complete the hypothesis test using a significance level of 5% and analyze your results. Show all of your work!

Step 4: State your conclusion. What was the result of your hypothesis test? Give your final decision AND provide an interpretation in the context of this problem. Include all important details.

Step 5: Confidence Interval Now that you have tested the company’s claim and have come to some conclusion about it, you may be wondering, what really is the true portion of all these candies that are the color I chose? Create a 95% confidence interval to help you answer that question.Show all of your work!

Step 6: Write a sentence to describe the meaning of your confidence interval in the context of this problem. How does the interval you calculated compare to the company’s claim? Does it support the company’s claim or give evidence against it? How does this compare with the results of your hypothesis test?

Find the median, quartiles, and make a histogram for the following data.

1,3,3,3,3,3,3,4,4,4,4,4,4,5,6,7,7,7,9,10,10,10,11,12,12,13,14,14,14,15,16,17,17,17,17,18,19,19,21,22,23,25,27,27,29, 32,35,35,36,45

in 2010, the Maricopa Community College District's enrollment data showed the following breakdown of students by ethnicity: 54.9% White; 21.1% Hispanic; 7.9% Black; 4.5% Asian/Pacific Islander; 2.9% Native American; 8.8% Other. Information was collected from a random sample 0f 300 students in 2017 to determine whether or not the data has changed significantly. The sample data is given in the table below. At the  α=0.05 level of significance, test the claim that the ethnic breakdown of students at MCCCD has not changed significantly since 2010.

Which would be correct hypotheses for this test?

• H0:The breakdown of students by ethnicity has changed significantly since 2010 (i.e. the given distribution no longer fits); H1:The breakdwon of students by ethnicity has not changed significantly since 2010 (i.e. the given distribution still fits)
• H0:The breakdown of students by ethnicity has not changed significantly since 2010 (i.e. the given distribution still fits);  H1:The breakdown of students by ethnicity has changed significantly since 2010 (i.e. the given distribution no longer fits)
• H0:μ1=μ2;H1:μ1≠μ2
• H0:p1=p2;2H1:p1≠p2

Ethnicity of students in sample:

Test Statistic:



Give the P-value:



Which is the correct result:

• Do not Reject the Null Hypothesis
• Reject the Null Hypothesis

Which would be the appropriate conclusion?

• There is enough evidence to suggest that the breakdown of students by ethnicity has changed significantly since 2010.
• There is not enough evidence to suggest that the breakdown of students by ethnicity has changed significantly since 2010.

1. Describe a scenario where a researcher could use a Goodness of Fit Test to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use? (3 points)
2. Describe a scenario where a researcher could use a Test for Independence to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use? (3 points)
3. The Goodness of Fit Test and Test for Independence both use the same formula to calculate chi-square. Why? I.e., explain the logic of the test. (3 points)
4. Compare the Goodness of Fit Test and the Test for Independence in terms of the number of variables and levels of those that can be compared. In what ways are they similar or different? (3 points)
5. Describe how the Test for Independence and correlation are similar yet different. (3 points)

3.50

Passedix is a game of chance played with three fair dice. Players bet whether the sum of the faces shown on the dice will be above or below ten. During the late sixteenth century, the astronomer and mathematician Galileo Galilei was asked by the Grand Duke of Tuscany to explain why “the chance of throwing a 9 with three fair dice was less than that of throwing a 10.” (Interstat, Jan. 2004) The grand duke believed that the chance should be the same because “there are an equal number of partitions of the numbers 9 and 10.” Find the flaw in the Grand Duke’s reasoning and answer the question posed to Galileo. Hint: What the Grand Duke was saying is: There are six ways to get a 9: 1+2+6; 1+3+5; 1+4+4; 2+2+5; 2+3+4; 3+3+3. There are also six ways to get a 10: 1+3+6; 1+4+5; 2+2+6; 2+3+5; 2+4+4; 3+3+4. [10 pts] 3.56 Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd} B: {Sum of the numbers showing is 9, 11, or 12} Are events A and B independent? Why? [10 pts]

How would an error in the application of a "treatment" impact the results of a study....provide an example.

To improve turnover (employees leaving your organization), you implemented a new training program company-wide about a year ago. However, you're not sure that the training is equally effective in reducing turnover between your service department, sales departments, and warehouse. To test this, you retrieved a list of all current and former employees that have received the training and created a dataset also recording their department. Conduct a test of independence to investigate this.

Turnover: Department:

former warehouse

current service

current sales

former warehouse

current sales

former sales

current sales

current service

former warehouse

current sales

current service

current warehouse

current service

current warehouse

current service

former sales

former sales

former service

The p-value for this chi-square was _____________and the chi-square value was _______________. This test _____________ achieve statistical significance. The expected value for Former Employee/Service was_________________, while the observed value was _______________________

options to fill in the blanks:

0.03, did, 2.33, did not, 0.33, 2.23, 1, 1.98.

The commercial division of a real estate firm conducted a study to determine the extent of the relationship between annual gross rents ($1000s) and the selling price ($1000s) for apartment buildings. Data were collected on several properties sold. The data is...

(a) How many apartments are there?
(b) Write the estimated regression equation
(c) Use the t-test to determine whether the selling price is related to annual gross rents. Use a=0.05
(d) Use the f-test to determine whether the selling price is related to annual gross rents. Use a=0.05
(e) Predict the selling price of an apartment building with gross annual rents of $52500

For each of the following situations, explain whether the binomial distribution applies for X.

a. You are bidding on four items available on eBay. You think that you will win the first bid with probability 25% and the second through fourth bids with probability 30%. Let X denote the number of winning bids out of the four items you bid on.

b. You are bidding on four items available on eBay. Each bid is for $70, and you think there is a 25% chance of winning a bid, with bids being independent events. Let X be the total amount of money you pay for your winning bids.

In a question involving a hypothesis test having the population mean as the target parameter, you are given the sample size, n, the assumed population mean, the significance of the test, alpha, whether it is a right-tailed, left-tailed, or two-tailed test, and the result of the test (reject or do not reject the null hypothesis.)

Show how you can use this information to find bounds on the sample itself. You may put in simple values for the information given if your prefer that to working directly with the formulas.

Suppose you were also given the P-value. Show how to obtain the test statistic from this, and the sample mean itself.

In another case –control study researchers investigated cleft lip with or without cleft palate by smoking status in those participants who reported consuming folic acid supplements. In this sub-group there were 42 cases of cleft lip with or without cleft palate and 55 controls who were current smokers; and there were 72 cases of cleft lip with or without cleft palate and 190 controls who were non-smokers.”

(a) “Construct a 2x2 table with columns and rows headings and calculate an appropriate measure of the strength of association between smoking and cleft lip with or without cleft palate in those who consumed folic acid supplements during pregnancy.” [4 marks]

b) “Interpret the findings in (a) in your own words.” [2 marks]

c) “What proportion of cleft lip with or without cleft palate in the population is potentially preventable, assuming a causal association between smoking and cleft lip.”[4 marks] explain in words your findings

Using the following sample data; 6, 7, 11, 6, 11, 5, 15, 11, 5;

Compute the sample standard deviation using either the computing formula or the defining formula.