"A test to determine whether a certain antibody is present is 99.6​% effective. This means that the test will accurately come back negative if the antibody is not present​ (in the test​ subject) 99.6​% of the time. The probability of a test coming back positive when the antibody is not present​ (a false​ positive) is 0.004. Suppose the test is given to five randomly selected people who do not have the antibody. ​(a) What is the probability that the test comes back negative for all five ​people? ​(b) What is the probability that the test comes back positive for at least one of the five ​people?"

3. Rosa Diaz is one of the best detectives at the 99th precinct in Brooklyn. She averages 4.89 felony arrests a week. Assume a 5-day workweek.

   1. A) What is the probability that Rosa has 5 felony arrests in a week?

   2. B) What is the probability that Rosa has at least 3 felony arrests in a week?

   3. C) What is the probability that Rosa has between 5 and 10 felony arrests in a week exclusive?

   4. D) What is the probability that Rosa has 3 felony arrests in a day?

Problem 1

The time for an employee to complete a certain manufacturing task was was approximately Normally distributed with a mean of 138 seconds and a standard deviation of 39 seconds. Suppose you plan to take an SRS of 250 employees and look at the average manufacturing time.

a)       Determine the mean and standard deviation of the distribution of sample means.

b)      Calculate the probability of coming up with a sample that shows a manufacturing time of 114 seconds or less.

Problem 2

You want to research the cost of a certain trendy ergonomic chair. In your online search of the cost of that chair on 20 different sites, you note that the mean cost of the chair is $562. Assume that the SD of the chair among all sites is $74. Find the 90%, 95%, and 99% confidence intervals for the mean cost of this chair.

Look at the 95% confidence interval and say whether the following statement is true or false. “This interval describes the price of 95% for all chairs of this model that are being sold.” If you think this is incorrect, be sure to explain why.   

Problem 3

A credit card company wants to estimate the average length of client churn (turning over their card for a different one). In a sample of 5000 customers obtained at random from the company’s database, the mean churn is 418. The the standard deviation of the calls from that sample is 93. Provide the mean and SD of the distribution of this sample.

Problem 4

A web-based travel search engine is designed to complete searches for cruise ships involving price retrieval and scheduling information. You need to analyze how long it takes to complete a typical search. The search time for 2500 randomly selected searches is recorded and detreemined as sample mean = 0.94 seconds and sample standard deviation = 0.36 seconds. Choose the most typical value for C and provide the confidence interval.

15. To measure the relationship between anxiety level and test performance, a psychologist obtains a sample of n=7 college students from an introductory statistics course. The students sre asked to come to the laboratory 15 minutes before the final exam. In the lab, the psychologist record physiological measures of anxiety (heart rate, skin resistance, blood pressure, and so on) for each participant. In addition, the psychologist obtains the exam score for each participant.

Student Anxiety Rating Exam Score

A 3 81

B 4 83

C 7 80

D 6 81

E 2 87

F 7 82

G 5 79

a. Compute the Pearson correlation for the data. Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all steps and all parts of all answers. b. Is there a significant relationship between anxiety and exam score? Use a two-tailed test with alpha =.05. Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all steps and all parts of all answers.

Age   Browsing Time (min/wk)
34   372
48   198
24   469
33   387
43   262
58   85
20   469
49   192
64   86
55   119
46   233
36   345
35   357
29   415
37   327

​d) Check the residuals to see if the conditions for inference are met.

The equal spread condition IS/IS NOT satisfied because the scatterplot of the residuals against the predicted values shows NO PATTERN/A THICKENING OF THE SPREAD/A THINNING OF THE SPREAD/A CURVATURE.

.The nearly normal condition IS/IS NOT satisfied because the Normal probability plot SHOWS/DOES NOT SHOW an approximately straight line. ​ (This is also the case because a histogram of the residuals IS APPROXIMATELY/IS NOT unimodal and​symmetric.)

The outlier condition IS/IS NOT satisfied because the Normal probability plot SHOWS SOME/DOES NOT SHOW ANY extreme outliers.

A magazine uses a survey of readers to obtain customer satisfaction ratings for the nation's largest retailers. Each survey respondent is asked to rate a specified retailer in terms of six factors: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all six factors. Sample data representative of independent samples of Retailer A and Retailer B customers are shown below.

(a)

Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let μ₁ = population mean satisfaction score for Retailer A customers and μ₂ = population mean satisfaction score for Retailer B customers.)

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

(b)

Assume that experience with the satisfaction rating scale of the magazine indicates that a population standard deviation of 11 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

At a 0.05 level of significance what is your conclusion?

Reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.    Do not Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Do not reject H₀. There is insufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.

(c)

Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Round your answers to two decimal places.)

to

Which retailer, if either, appears to have the greater customer satisfaction?

The 95% confidence interval  ---Select--- is completely below is completely above contains zero. This suggests that the Retailer A has a  ---Select--- higher lower population mean customer satisfaction score than Retailer B.

An automatic filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of s2 = 0.01532 (fluid ounce). If the variance of fill volume is too large, an unacceptable proportion of bottles will be under- or overfilled. We will assume that the fill volume is approximately normally distributed. Determine the 95% upper confidence bound of the variance.

1. A study compared patients who suffered a heart attack in the daytime with patients who suffered a heart attack in the night.  Of 58,593 had a heart attack in the daytime 11,604 survived.  Of 28,155 who had a heart attack at night 4139 survived.  Use α = .01 and test the claim that the survival rates are the same.

Important: please show work for each question. Thank you!

In a previous section of PSY230, the second exam was worth 80 points. The scores from that class were normally distributed with a mean (μ ) of 65 and a standard deviation (σ) of 5. If the exam scores were converted to a Z distribution, the distribution would form a perfect bell shape. The following questions require locating individual exam scores on the Z distribution and examine the percentage (or proportion) of cases above or below a score.

Hints: It helps to draw a Z distribution (bell curve) and place John’s and Tom’s Z scores on the distribution for answering the questions. Use the Z table for converting between Z score and area (percentage) of the distribution.

1. John obtained a score of 74. What is John’s z score?

2. What is the percentage of the students that scored higher than John?

3. If 50 students were in that class, about how many of them scored lower than John’s score? (You can round your answer to the nearest whole number.)

4. Tom obtained a score of 59. What is Tom’s z score?

5. What is the percentage of students that scored between John and Tom?

6. There are 50 students in the class, so about how many of them would likely score lower than Tom? (You can round your answer to the nearest whole number.)

7. Anna only knows that she scores at 87^th percentile on this exam, what is her z score?

8. Based on the result of the previous question, what would be Anna’s actual score on the exam?

The organisation ‘Australian Hearing’, an agency of the federal government, published a report on ‘binge listening’. As part of the research for the report, they carried out a survey, which was described as follows:

'One thousand Australians aged between 18 and 35 years in metropolitan and regional locations in all states across all education levels participated in a 15- minute online survey. The questions related to their exposure to noise during leisure activities, their perception of noise, perceived causes of hearing loss and attitudes towards hearing protection. The research was conducted by Inside Story.'

Which one of the following propositions is reasonable, in the circumstances and given only the information provided in the paragraph?

a) Although there is not much detail in the description here, it is reasonable to assume that a survey conducted by a federal agency was well-conducted and that the results will be reliable.

b) The large sample size of 1000 means that the results will be unbiased.

c) The coverage of all areas and states in Australia and all education levels means that the result will be reliable.

d) The online mechanism used to provide responses was a reasonable way for the survey participants to provide their views.

For 2018, Charlie’s would like to discontinue one of the appetizers. Which one would you suggest they discontinue, and why do you make that recommendation? Find two different ways to do an analysis that leads you to two different conclusions. (Using regression, correlation or descriptive stats)

1. The U.S. Postal Service (USPS) has used optical character recognition (OCR) since the mid-1960s. In 1983, USPS began deploying the technology to major post offices throughout the country (www.britannica.com). Suppose that in a random sample of 500 handwritten zip code digits, 466 were read correctly.

Note: Optical Character Recognition, or OCR, is a technology that enables you to convert different types of documents, such as scanned paper documents, PDF files or images captured by a digital camera into editable and searchable data.

Source: Montgomery, D. & Runger, G. (2014). Applied Statistics and Probability for Engineers. 6^th edition, Hoboken, NJ: Wiley.

Using RStudio, construct and interpret a 95% confidence interval for the true proportion of correct digits that can be automatically read by OCR technology in USPS.

1. Label the parameter. (4 points)

2. Propose an appropriate confidence interval. (4 points)

3. Verify the required conditions for the proposed confidence interval. (8 points)

4. Report a 95% confidence interval (simulation base for the true proportion of correct digits that can be automatically read by OCR technology in USPS. Use seed = 45678 and 40,000 trials for simulation: (5 points)

Note: Report CI (3 decimal places):

Note: Attach your R codes in the following space:

5. Interpret a 95% confidence interval for the true proportion of correct digits that can be automatically read by OCR technology in USPS in context. (6 points)

The Director of Acquisition marketing for L.L. Bean is testing a series of new email lists and comparing it to a cross section of her usual lists to serve as a control. To do this she set up a spread sheet and computed the test statistic and pvalue of all of the test lists as compared to the control. The test statistics are representative to a two tailed hypothesis test where H_o: u₁= u₂ vs H_a: u₁ ≠ u₂.The results are shown below:

a. Compute the pvalue for the Apparel shoppers opt in list. Note that the pvalue for the open rate and the click rate are both missing.

b. All comparisons are made relative to the control. Answer what is the best test list for click rate. Is it the best directionally or with statistical significance?

c. All comparisons are made relative to the control. Answer what is the worst test list for open rate. Is it the worst directionally or with statistical significance?

A service process has three serial stages. The defect percentage at stage one is 7%. The defect percentage at stage two is 13%. And, the defect percentage at stage three is 15%. Use 5 decimals for probabilities and 2 decimals for sigma levels in the following situations. (a)[2] Situation A: the connection logic of the three stages is that a good overall outcome only happens if all three stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. Using Excel, calculate the corresponding sigma level and make a statement. (b)[2] Situation B: the connection logic of the three stages is that a good overall outcome happens when at least one stage has good outcome. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. Calculate the corresponding sigma level and make a statement. (c)[3] Situation C: the connection logic of the three stages is that a good overall outcome happens when at least two stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. Calculate the corresponding sigma level and make a statement. (d)[3] Give some possible real‐life processes for the three situations above.

Below are the number of hours spent exercising:

1. Which descriptive statistics from your output would you NOT report for Hours spent Exercising? Why not?

2. Write a few sentences describing the data (use APA formatting). This interpretation should not include only the numbers, but rather what the numbers tell you about the data.

3. Create a histogram for the hours spent exercising. You can do this by hand or via computer. If you do it by hand simply take a picture and upload it along with your assignment.

4. If you add 4 points to each exercise score, what will the mean and standard deviation be for this variable?

Hint: You shouldn’t have to recalculate from the raw data to answer questions 7 & 8.

5. If you subtract 1 point from each exercise score, what will the mean and standard deviation be for this variable?
6. Give one example of data for each of the following and explain why?

1. When the median is more appropriate to use than the mean

2. When the mean is more appropriate to use than the median

3. When you would expect high variability

4. When you would expect low variability

7. When describing nominal data, which measure of central tendency is appropriate?

8. Why do we subtract 1 from the number of scores when calculating variance and standard deviation?

9. Describe how would you calculate standard deviation if you know variance?