1. A prison administrator is interested in examining the relationships between the type of prison security (maximum, medium, and minimum) and the number of previous offenses committed by an inmate. He believes that maximum security prisons have inmates with many prior offenses, medium security with not so many offenses, and minimum security with almost no prior offenses. He randomly selects eight new inmates from each of the three security levels and compares the number of offenses for which they have ever been charged.

a) What is the independent variable?              

b) What is the dependent variable?

c) What is the null hypothesis?

d) What is the research hypothesis?

e) Interpret the results.

Maximum	Medium	Minimum
8	4	2
6	4	2
4	3	3
5	6	2
3	5	4
7	6	1
6	3	2
9	3	2

A researcher did a study looking at the effectiveness of different approaches to washing leafy green produce, with the goal of reducing risk for Escherichia coli (e coli) exposure in consumers. Farms were randomly assigned to either an enhanced washing regimen for three months, or to an industry-standard washing approach for the same amount of time. Periodically a member of a research team would visit each farm and obtain a sample of leafy greens for testing. The primary measure collected was the total number (count) of e-coli tainted samples collected from each farm over the three month period. There were 16 farms assigned randomly to each group. The distributions of e coli counts are below.

Typical washing: 6, 5, 9, 1, 0, 6, 2, 19, 3, 2, 1, 0, 1, 3, 6, 5

Enhanced washing: 2, 0, 3, 0, 0, 6, 3, 2, 0, 3, 0, 2, 2, 3, 1, 0

Compute the 95% Confidence Intervals for the each group, and then the CI 95% for the difference between the 2 groups. Using your CI 95% findings for the enhanced washing group, what is the margin of error? What is the standard error? Provide a brief narrative description for each CI you calculate.

A NAPA auto parts supplier wants information about how long car owners plan to keep their cars. a simple random sample of 31 car owners results in a mean of 7.01 years and a standard deviation of 3.74 years, respectively. Assume the sample is drawn from a normally distributed population.

a) Find a 95%confidence interval estimate of the mean.

b) Find a 95% confidence interval estimate of the population standard deviation.

c) If several years pass and you want to conduct a new survey to estimate the mean length of time that car owners plan to keep their cars, how many randomly selected cars owners must you survey? Assume you want 99% confidence that the sample mean is within 0.25 year of the population mean,also assume the standard deviation is 3.74 years.

Consider the following set of ordered pairs. x 4 2 4 3 6 4 y 5 7 7 4 2 7 ​a) Calculate the correlation coefficient. ​b) Using alpha equals 0.05​, perform a hypothesis test to determine if the population correlation coefficient is less than zero. LOADING... Click the icon to view a portion of the​ Student's t-distribution table. ​a) requals nothing ​(Round to three decimal places as​ needed.) ​b) Determine the null and alternative hypotheses. Upper H 0​: rho ▼ less than or equals greater than or equals less than greater than not equals equals 0 Upper H 1​: rho ▼ greater than less than or equals equals less than not equals greater than or equals 0 The​ t-test statistic is nothing. ​(Round to three decimal places as​ needed.) The critical​ t-score(s) is(are) nothing. ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.) Because the test statistic is ▼ equal to less than greater than the critical​ value, ▼ do not reject reject the ▼ alternative hypothesis. null hypothesis. One ▼ cannot can conclude that the population correlation coefficient is ▼ equal to not equal to greater than less than zero.

As per the author, Hirschey, how are the following methods used to effectively answer the question, What do customers want?: consumer Interviews, surveys, market experiments and regression analysis.

A fast food company uses two management-training methods. Method 1 is a traditional method of training and Method 2 is a new and innovative method. The company has just hired 40 new management trainees. Nineteen of the trainees are randomly selected and assigned to the first method, and the remaining twenty-one trainees are assigned to the second training method. After three months of training, the management trainees took a standardized test. The test was designed to evaluate their performance and learning from training. The sample mean test score and sample standard deviation of the two methods are given below. The management wants to determine if the company should implement the new training method. Using α = .025, is the average test score for the traditional method significantly lower than the average test score for the innovative method? Do a complete and appropriate hypothesis test.

	Sample Mean	Sample standard deviation
Population 1: Method 1 (traditional)	83	2.7
Population 2: Method 2 (innovative)	81	3.3

H₀: (Click to select)p1π1σ1n1s1μ1x-bar1 (Click to select)=≠≤>≥< (Click to select)s2x-bar2π2n2p2σ2μ2

H_A: (Click to select)μ1x-bar1π1p1σ1s1n1 (Click to select)=≠≤>≥< (Click to select)μ2x-bar2π2p2σ2s2n2

Using only the appropriate statistical table in your textbook, the critical value for rejecting H₀ is (Click to select)+-± . (report your answer to 3 decimal places, using conventional rounding rules)

Using the sample data, the calculated value of the test statistic is (Click to select)+-± . (report your answer to 2 decimal places, using conventional rounding rules)

Should the null hypothesis be rejected? (Click to select)yes or no

Should the management conclude that the average test score for the traditional method is significantly lower than the average test score for the innovative method? yes or no

Using only the appropriate statistical table in your textbook, what is the most accurate statement you can make about the numerical value of the p-value of this hypothesis test?      

Answer: ____________________________________________________________________________ (provide a one-sentence statement about the p-value)

A treadmill manufacturer has developed a new machine with softer tread and better fans than its current model. The manufacturer believes these new features will enable runners to run for longer times than they can on its current machines. To determine whether the desired result is achieved, the manufacturer randomly sampled 10 runners. Each runner was measured for one week on the current treadmill and for one week on the new treadmill. The weekly total number of minutes for each runner on the two types of treadmills was collected, and is provided in the table below.

Runner	New treadmill (minutes run)	Current treadmill (minutes run)
1	269	270
2	280	268
3	260	254
4	271	256
5	273	258
6	264	264
7	263	262
8	260	251
9	263	264
10	274	258

Construct a 98% confidence interval estimate of the mean difference in running time (in minutes) on the new and current treadmills.

ANSWER:  (Click to select)-±+  ≤ (Click to select)(μ1 - μ2)(n1 - n2)(σ1 - σ2)μd(p1 - p2)(s1 - s2)(π1 - π2)(x-bar1 - x-bar2) ≤ (Click to select)±+-  (report your answers to 2 decimal places, using conventional rounding rules.)

Consider the following hypothesis test.

H₀: μ ≤ 12

H_a: μ > 12

A sample of 25 provided a sample mean

x = 14

and a sample standard deviation

s = 4.37.

(a)

Compute the value of the test statistic. (Round your answer to three decimal places.)

(b)

Use the t distribution table to compute a range for the p-value.

p-value > 0.200

0.100 < p-value < 0.200    

0.050 < p-value < 0.100

0.025 < p-value < 0.050

0.010 < p-value < 0.025

p-value < 0.010

(c)

At

α = 0.05,

what is your conclusion?

Reject H₀. There is sufficient evidence to conclude that μ > 12.

Do not reject H₀. There is sufficient evidence to conclude that μ > 12.    

Do not reject H₀. There is insufficient evidence to conclude that μ > 12.

Reject H₀. There is insufficient evidence to conclude that μ > 12.

(d)

What is the rejection rule using the critical value? (If the test is one-tailed, enter NONE for the unused tail. Round your answer to three decimal places.)

test statistic≤

test statistic≥

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that μ > 12.

Do not reject H₀. There is sufficient evidence to conclude that μ > 12.    

Do not reject H₀. There is insufficient evidence to conclude that μ > 12.

Reject H₀. There is insufficient evidence to conclude that μ > 12.

Question 7

Acid rain is an environmental challenge in many places around the world. It refers to rain or any other form of precipitation that is unusually acidic, i.e. rainwater having elevated levels of hydrogen ions (low pH). The measure of pH is a measure of the acidity or basicity of a solution and has a scale ranging from 0 to 14. Distilled water, with carbon dioxide removed, has a neutral pH level of 7. Liquids with a pH less than 7 are acidic. However, even unpolluted rainwater is slightly acidic with pH varying between 5.2 to 6.0 due to the fact that carbon dioxide and water in the air react together to form carbonic acid. Thus, rainwater is only considered acidic if the pH level is less than 5.2..

In a remote region of Algonquin Park, a biologist measured the pH levels of rainwater and obtained the following data for 16 rainwater samples on 16 different lakes:

4.73	4.79	4.87	4.88
5.04	5.06	5.07	5.09
5.11	5.16	5.18	5.21
5.23	5.24	5.25	5.25

Is there reason to believe that the is considered acidic (less than 5.20)?

Use the Sign Test to test the claim at 95% confidence that the rainwater from this region has a median pH level less than 5.20.

a) State the Hypotheses (1)

b) State the decision rule (1)

c) Determine the test statistic (1)

d) State your decision and interpretation. (1,1)

A company has developed a forecast using the Delphi method for January through June

1. Using the data provided, what is the Mean Absolute Deviation for the forecast method?

2. Using the data provided, what is the MAPD?

Month	Demand	Forecast
January	232	234
February	225	222
March	239	240
April	260	261
May	234	231
June	260	262

Assume Monthly Advertising Expenditure is the independent variable.

Store	Monthly Profit	Monthly Advertising expenditure
A1	$13,593.02	$1,710.00
A2	$23,896.73	$1,983.00
A3	$9,932.64	$952.00
A4	$9,100.41	$1,009.00
A5	$15,220.08	$2,315.00
A6	$33,900.67	$2,197.00
A7	$6,935.36	$934.00
A8	$10,112.62	$2,375.00
A9	$9,155.14	$1,065.00
A10	$8,513.94	$812.00
A11	$7,933.25	$1,052.00
A12	$11,388.13	$2,234.00
A13	$26,299.72	$2,962.00
A14	$21,423.87	$1,699.00
A15	$21,430.21	$1,991.00
A16	$19,984.96	$2,181.00
A17	$11,575.09	$1,831.00
A18	$18,900.44	$1,819.00
A19	$21,815.24	$2,394.00
A20	$35,642.73	$2,296.00

What is the sum of squares total value?

	Friendly	Cooperative	Impatient	Total
Male	674	166	40	800
Female	886	161	38	1085
Total	1560	327	78	1965

The table shows a cross tabulation of two variables, gender and the attitudes of the survey respondents towards the interviewers who collected data from them.

Can you conclude with at least 95% confidence that gender and respondent attitudes towards the interviewers are related? Explain why.

The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure, and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed.

Refer to Exhibit 8-2. Construct a 90% confidence interval for the mean duration of the foreclosure process in Boston.

[259.7400, 405.7600]

[293.2137, 372.2863]

[298.4296, 367.0704]

[303.2282, 362.2718]

Text book: Essentials of Biostatistics in Public Health 3 ed. by Lisa Sullivan.

Instructor provided problem: An observational study is conducted to compare experiences of men and women between the ages of 50-59 years following coronary artery bypass surgery. Participants undergo the surgery and are followed until the time of death, until they are lost to follow-up or up to 30 years, whichever comes first. The following table details the experiences of participating men and women. The data below are years of death or years of last contact for men and women. Estimate the Estimate the survival functions for each treatment group using the Kaplan-Meier approach. Test if there is a significant difference in survival between treatment groups using the log rank test and a 5% level of significance.

Men			Women
Year of Death	Year of Last Contact		Year of Death	Year of Last Contact
5	8		19	4
12	17		20	9
14	24		21	14
23	26		24	15
29	26			17
	27			19
	29			21
	30			22
	30			24
	30			25
				30

Beer bottles are filled so that they contain an average of 385 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 9 ml. Use Table 1.

a.	What is the probability that a randomly selected bottle will have less than 380 ml of beer?(Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability

b.	What is the probability that a randomly selected 7-pack of beer will have a mean amount less than 380 ml? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability

c.	What is the probability that a randomly selected 24-pack of beer will have a mean amount less than 380 ml? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)