A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 ounces with a standard deviation of .1 ounces. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the means calculated should occur in what interval? Hint: the standard deviation rule says that 95% of the observations are within how many standard deviations away from the mean? Round answers to four decimal places

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1.) Consideration of Causation:

(i) Describe a realistic, but a hypothetical example of a situation in public administration where a novice researcher might incorrectly think that a clear correlation between two variables implies that one caused the other.?

(ii) Then, discuss the correct research-based approach to the analysis of your hypothetical example. In other words, how should the relationship between the two variables be accurately described or approached by a seasoned researcher?

2. Earlier in this chapter, we discussed that iron supplements are popular in part because they raise oxygen levels in our bodies, and increased oxygen levels help us feel more energetic. We also said that consuming an iron supplement with a drink high in Vitamin C enhances the effects of the iron supplement. A researcher has a sample of 40 people randomly assigned to two factors: iron supplement and Vitamin C consumption. Specifically, people were randomly assigned either to take an iron supplement or not to take an iron supplement. In addition, people were also randomly assigned either to consume a glass of orange juice (which is high in Vitamin C) or not to consume a glass of orange juice. The researcher uses a pulse oximetry to measure oxygen levels as the dependent variable (to keep the calculations simple, we are using intentionally hypothetical numbers for oxygen levels).The data is presented below. Carry out the analysis of variance using SPSS and determine whether there are any main effects or an interaction. Make a line graph of the results and interpret the pattern of the results.

The time until the light in Bob's office fails is exponentially distributed with mean 2 hours. The time until the computer crashes in Bob's office is exponentially distributed with mean 3 hours. Failure and crash times are independent.

(a) Find the probability that neither the light nor computer fail in the next 2 hours

(b) Find the probability that the computer crashes at least 1 hour after the light fails.

8. Adam, Bonnie, Chuck, Dave and Elaine are engineers from different companies attending a professional conference at the University of Arizona in Tucson. There are seven hotels near the campus. Each engineer will stay at a randomly picked hotel. a. What is the probability that they will all stay at the same hotel? b. What is the probability that they will all stay at different hotels? c. Adam has a crush on Bonnie, what is the probability that they will stay at the same hotel? d. What is the probability that exactly two of the five engineers will stay at the same hotel with no one else staying at a same hotel?

At a recent halloween party, the women appeared to be consuming more packages of halloween candy than were the men. If the mean number of packages consumed by the 3 men was 4, and that for the 7 women was 6, and the standard deviation for the whole group was 2 packages, what was the correlation between gender and the number of packages consumed?

I had used the the point-biserial correlation coefficient equation and had gotten 0.46. Is this correct? Also does this mean that it is a substantially high correlation or is it quite low?

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Suppose we have the following information. Note: In 1851 there were 25,466 nurses in Great Britain. Age range (yr) 20-29 30-39 40-49 50-59 60-69 70-79 80+ Midpoint x 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.9% 9.1% 19.1% 29.9% 25.5% 8.8% 1.7% (a) Using the age midpoints x and the percent of nurses, do we have a valid probability distribution? Explain. No. The events are indistinct and the probabilities do not sum to 1. Yes. The events are distinct and the probabilities sum to 1. No. The events are indistinct and the probabilities sum to 1. Yes. The events are distinct and the probabilities do not sum to 1. (b) Use a histogram to graph the probability distribution in part (a). Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (c) Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older. (Round your answer to three decimal places.) (d) Compute the expected age μ of a British nurse contemporary to Florence Nightingale. (Round your answer to two decimal places.) yr (e) Compute the standard deviation σ for ages of nurses shown in the distribution. (Round your answer to two decimal places.) yr

Produce a Pareto diagram that shows total spending in a descending order and at the same time the cumulative percentage curve.
Based on the above, can you estimate which part of visitors accounts for 75% of total revenues in the island.

The data used are:

1. The provost at the University of Chicago claimed that the entering class this year is larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year’s entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The University’s record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. Round final answers to two decimal places. Solutions only.

(A) The parameter the president is interested in is:
(a) the mean number of entering students to his university this year.
(b) the mean number of entering students to all U.S. universities this year.
(c) the mean SAT score of the entering students to his university this year.
(d) the mean SAT score of the entering students to all U.S. universities this year.

(e) None of the above.

(B) The population the president is interested in is:
(a) all entering students to all universities in the U.S this year.

(b) all entering students to his university this year.
(c) all SAT test centers in the U.S. this year.
(d) the SAT scores of all students entering universities in the U.S. this year.

(e) None of the above.

(F) True, False, or Uncertain: The null hypothesis would be rejected.

(G) True, False, or Uncertain: The null hypothesis would be rejected if a 10% probability of committing a Type I error is allowed.

(I) True, False, or Uncertain: The evidence proves beyond a doubt that the mean SAT score of the entering class this year is lower than previous years.

(J) True, False, or Uncertain: If these data were used to perform a two-tail test, the p-value would be 0.1254.

1.A group of psychologists is interested in determining if private practice doctors and hospital doctors have the same distribution of working hours. They survey 150 private practice doctors and 150 hospital doctors (selected at random) and asked about the number of hours per week they worked Determine whether there is a difference in hours worked per week for private practice and hospital doctors.

1. What kind of statistical test will you be performing?

2. Will you need to test for equal variance? If so, what are your results and how does that influence the next steps in your analysis?

3. What are your null and alternative hypotheses?

H₀:

H_A:

4. Discuss the results of your analysis. Will you accept or reject your null hypothesis? Why? What can you specifically say about the data?

Suppose the length of time a person takes to use an ATM at the bank is normally distributed with mean of 110 seconds and standard deviation of 10 seconds. There are 4 people ahead of you in the queue waiting to use the machine. You are concerned about the total time (T) the 4 people ahead of you will take to use the machine.

(i) What is the mean value of T, the total time (in seconds) for the 4 people ahead of you to use the machine?

(ii) Assuming that the times for the 4 people are independent of each other, determine the standard deviation of T. (remember 20 x 20 = 400) (iii) Sketch the distribution for T, clearly labelling the important features on your sketch.

(iv) Use your sketch and the Empirical rule (0.68 within 1 standard deviation of the mean, 0.95 within 2 standard deviations of the mean, 0.997 within 3 standard deviations of the mean in a normal population) to find the probability that the total time T is less than 400 seconds.

Approximately 35.73% of all businesses are owned by women. If you take a sample of 105 businesses in Michigan, what is the probability that less than 32.92% of them would be owned by women?

Question 4 options:

Energetic Co., a battery manufacturer, claims their battery lasts for 67.37 months with a standard deviation of 11.583 months. You randomly sample 16 of these batteries. Assuming the distribution for the battery lifetime is approximately normal, what is the probability the average lifetime is greater than 66.54?

Question 9 options:

The F distribution differs from the t distribution is all of these ways except ?

(1 point) A recent poll of 2300 randomly selected 18-25-year-olds revealed that 266 currently use marijuana or hashish. According to a publication, 12.5% of 18-25-year-olds were current users of marijuana or hashish in 1997. Do the data provide sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%? Use α=0.01 significance level.

test statistic z=

positive critical z score    

negative critical z score     

The final conclusion is

A. There is not sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%.
B. There is sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%.

The following is a short description of the 1854 cholera epidemic of London investigated by Dr. John Snow. Read it and answer the questions that follow.

A total of 862 out of 186,787 people died due to cholera in a sub-district of London during a 48 day period from July 8 to August 26,1854. 844 cholera deaths occurred in a sub-population of 167,654 people using water supplied by Southwark Company, while 18 cholera deaths occurred in 19,133 people using water supplied by Lambeth Company. Dr. John Snow conducted a study of the area and found that each company supplied both rich and poor, both large and small houses, and there were no differences in either the health condition or occupation of the persons receiving the water of the two companies. On the basis of these findings, John Snow argued that drinking water supplied by Southwark Company, whose source was the polluted water of the Thames River, caused the cholera epidemic. Cholera deaths decreased after the water source was changed to less polluted water.

1. Calculate the risk ratio of cholera deaths among people using water supplied by Southwark Company as compared to Lambeth Company.

2. Do you think that this risk ratio is strong enough to support a cause-effect relationship between cholera deaths and water supply? Why or why not?

3. John Snow's study was done long before the identification of the causative organism of cholera-- Vibrio cholera. Thus, Sir Bradford Hill's guideline of biological plausibility was lacking when John Snow did his study. What does this tell you about the nature of the biological plausibility criteria?

4. As you know, temporality is one of the key causal guidelines proposed by Hill. What kind of evidence would need to be provided about the 1854 cholera epidemic to support Hill's guideline about temporality?

5. A marked reduction in cholera deaths occurred after the improvement in water supply. Which one of Hill's guidelines is supported by this fact?