2. What is the sample size, n, for a 95% confidence interval on the mean, if we know that the process’ standard error is 3.2 units, and we want to allow at most 1.0 units for our error?

3. Let’s say that you just randomly pulled 32 widgets from your production line and you determined that you need a sample size of 46 widgets, However, you get delayed in being able to pull another bunch of widgets from the line until the start of the next day. How many widgets should you now pull for your analysis?

4. What is the sample size, n, for a 98% confidence interval on the mean, if we know that the process’ standard error is 3.2 units, and we want to allow at most 0.5 units for our error?

5. What is the sample size, n, for a 95% confidence interval on the mean, if we know that the process’ standard error is 3.2 units, and we want to allow at most 0.5 units for our error?

According to published reports, practice under fatigued conditions distorts mechanisms that govern performance. An experiment was conducted using
15 college males, who were trained to make a continuous horizontal right-to-left arm movement from a microswitch to a barrier, knocking over the barrier coincident with the arrival of a clock sweephand to the 6 o’clock position. Theabsolute value of the difference between the times, in milliseconds, that it took to knock over the barrier and the time for the sweephand to reach the 6 o’clockposition (500 msec) was recorded. Each participant performed the task five times under prefatigue and postfatigue conditions, and the sums of the absolute differences for the five performances were recorded. The data can be found in the folder of this question.

1. a) (0.5 point) Read the data into R using read.csv function. Note: Show your codes but not the result/output.

2. b) (0.5 point) An increase in the mean absolute time difference when the task is performed under postfatigue conditions would support the claim that practice under fatigued conditions distorts mechanisms that govern performance. Assuming the populations to be normally distributed, write the two hypothesis of interest to test this claim.

c) (1 point) Use a suitable test in R to test your hypothesis in (b). Show your codes, output and use α = 0.05.

d) (1 point) Interpret your finding in (c).

data:

Prefatigue,Postfatigue
159,92
93,60
66,216
99,227
34,224
90,92
149,93
59,178
143,135
118,117
75,154
67,220
110,144
58,165
86,101

A machine that puts corn flakes into boxes is adjusted to put an average of 15.1 ounces into each box, with standard deviation of 0.23 ounce. If a random sample of 15 boxes gave a sample standard deviation of 0.35 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment? (Use a 0.01 level of significance.)

(i) Give the value of the level of significance.


State the null and alternate hypotheses.

H₀: σ² < 0.0529; H₁: σ² = 0.0529

H₀: σ² = 0.0529; H₁: σ² ≠ 0.0529

    H₀: σ² = 0.0529; H₁: σ² < 0.0529

H₀: σ² = 0.0529; H₁: σ² > 0.0529

(ii) Find the sample test statistic. (Round your answer to two decimal places.)


(iii) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000

.050 < P-value < 0.100

    0.025 < P-value < 0.0500

.010 < P-value < 0.0250

.005 < P-value < 0.010

P-value < 0.005

(iv) Conclude the test.

Since the P-value ≥ α, we fail to reject the null hypothesis.

Since the P-value < α, we reject the null hypothesis.

   Since the P-value < α, we fail to reject the null hypothesis

.Since the P-value ≥ α, we reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is sufficient evidence to conclude that the variance has increased and the machine needs to be adjusted.

At the 1% level of significance, there is insufficient evidence to conclude that the variance has increased and the machine needs to be adjusted.    

Results from the National Health Interview Survey show that among the U.S. adult population, 45.9% do not meet physical activity guidelines, 3.5% meet only strength activity, 29.0% meet only aerobic activity, and 21.6% meet both strength and aerobic activity. We sampled 4475 adults from Ohio and the results were as follows: 50.0% do not meet physical activity guidelines, 5.0% meet only strength activity, 35.0% meet only aerobic activity, and 10.0% meet both strength and aerobic activity. Conduct an appropriate hypothesis test to determine if the distribution in physical activity among Ohioans is similar to the U.S. population. Interpret your results.

PLEASE USE RULES OF ADDITION OF PROBABILITY

/MDPART 1: Create a context: Introduce a real-world business situation or an imagined business scenario that may benefit from the theories and methods presented in the prior two weeks (Weeks 3 and 4 - see the objective stated in bold above). While creating the context, ask yourself: What business use cases may benefit from the quantitative methods offered last week and this week? Pick one. You can use Google or other search tools, or your own workplace experience, to create the context. Once you decide on the context, describe it clearly in your PPT presentation. Be sure to deliver all relevant information for the audience (in this case your instructor) to help him/her understand the context fully.

Part 2: Show with examples how the quantitative methodology introduced in the prior two weeks relate to the business use case you introduced. (e.g., does the math/methodology help to resolve a business problem?) Be specific in your description of how you can use the quantitative information in connection with the business case (your context) you described. Give examples. Use technical terminology when necessary.

Part 3: Reflect on your learning by answering these questions: What changes have you observed in your own learning or knowledge of math/quantitative methods as a result of the topics introduced in Weeks 3 and 4 of this course? What did you find most valuable or useful for your MBA education and/or your current/future career. (As you articulate your thoughts for

Part 3, be original: Do not repeat the business context or situation you described in Parts 1 and 2. Think beyond that context

To use Excel INV functions, such as XXXX.INV(probability,....) to generate random variates, replace probability by:

For the following situation identify the sampling method used.

The Florida Fish and Wildlife Conservation Commission manatee mortality database website has information on cause of death and size for all manatees killed off Florida waters.We decide to divide the cause of death into watercraft, natural causes, stress, and other. Within each of these groups, a random sample of 25 manatees are selected.

Use the data for two Sydney suburbs to answer questions 1-5:            

1     Using Excel or other appropriate software, produce two separate histograms for the median rental prices of the two selected suburbs, respectively.    

       Use an appropriate number of bins for your histogram and remember to label the axes. Describe and compare the two histograms, including the central location, dispersion and skewness. [1 mark]     

2     Compute the sample means and sample standard deviations of the median rental prices of the two selected suburbs, respectively. No need to show computational steps. [1 mark]   

I am having trouble with all three parts.

A shelf contains 3 novels, 2 books of poetry, and 1 dictionary. We select 2 books at random in turn without replacement. Define events A and N by: A = “the dictionary is selected”, N = “at least one novel is selected”. Show your work to find each of the following:

(a) P(A' )

(b) P(N)

(c) P(A ∩ N).

An outbreak of Salmonella-related illness was attributed to ice cream produced at a certain factory. Scientists are interested to know whether the mean level of Salmonella in the ice cream is greater than 0.2 MPN/g. A random sample of 20 batches of ice cream was selected and the level of Salmonella measured. The levels (in MPN/g) were:

0.593, 0.142, 0.329, 0.691, 0.231, 0.793, 0.519, 0.392, 0.418, 0.219 0.684, 0.253, 0.439, 0.782, 0.333, 0.894, 0.623, 0.445, 0.521, 0.544

a) (0.5 point) Read the data in R using a vector. Show your codes only but not the output.

b) (0.5 point) State the two hypotheses of interest.

c) (1 point) Is there evidence that the mean level of Salmonella in the icecream is greater than 0.2 MPN/g? Assume a Normal distribution and use α =0.05. Show your codes and result/output from R.

d) (1 point) Interpret your finding in (c).

Hi there, I have put up the full sheet but it is question two that I need answered the most. Thank you for your time.

Question 1.

Drunk driving is one of the main causes of car accidents. Interviews with drunk drivers who were involved in accidents and survived revealed that one of the main problems is that drivers do not realise that they are impaired, thinking “I only had 1-2 drinks … I am OK to drive.” A sample of 5 drivers was chosen, and their reaction times (seconds) in an obstacle course were measured before and after drinking two beers. The purpose of this study was to check whether drivers are impaired after drinking two beers. Below is the data gathered from this study:

Driver 1 2 3 4 5

Before 6.15 2.86 4.55 3.94 4.19

After 6.85 4.78 5.57 4.01 5.72

1. The two measurements are dependent. Explain why. [1 mark]

2. Provide an estimate of the mean difference in reaction times between the two measurements. [4 marks]

3. Calculate and interpret a 95% confidence interval for the mean difference in reaction times between the two measurements. [15 marks]

4. Use a 5% level of significance and the following points to test the claim that reaction times before drinking two bears is lower than reaction times after drinking two bears.

(a) State the null and alternative hypotheses in symbolic form and in context.

(b) Calculate the test statistic.

(c) Identify the rejection region(s).

(d) Clearly state your conclusions (in context). [4 marks each]

5. What would the conclusion be if using a 1% level of significance? Justify your answer. [4 marks]

Question 2

This is part 2, this is the part that I need answered. Thank you for your time.

It was believed from the experiment on the obstacle course, in Part I, that there is a relationship between a subject’s reaction time before drinking two beers and the subject’s age:

Driver 1 2 3 4 5

Age (years) 20 30 25 27 26

1. What type of study is being outlined here? Justify your answer. [2 marks]

2. Plot a graph representing the relationship between reaction times before drinking two beers and age. [5 marks]

3. From the graph in Q2, suggest a relationship that could exist between the two measurements. [2 marks]

4. Use a 1% level of significance and the following points to test the claim that there is a relationship between the reaction times before drinking two beers and age.

(a) State the null and alternative hypotheses in context. [3 marks]

(b) Calculate the test statistic. [8 marks]

(c) Identify the rejection region(s). [4 marks]

(d) Clearly state your conclusions (in context). [4 marks]

5. What percentage of variation in reaction times before drinking two beers is unexplained by the relationship between reaction times before drinking two beers and age? [2 marks]

6. Derive a model/equation that could be used to predict reaction times before drinking two beers for a person, if the age of the person is known. [8 marks]

7. Using the model derived in Q6, what would the predicted reaction time, in the obstacle course, before drinking two beers of a 22-year-old be? [2 marks

Please correct chosen answers if incorrect.

22) d

23) c

24) c

22) Which of the following is not true regarding event rates:

a. an event can be anything such as Chicago Cubs winning the World Series

b. event rates are seldom used as they only provide data of nominal significance

c. event rate is statistical term that describes how often an event occurs

d. the formula for event rate is the number of times the event occurs, divided by the number of possible times the event could occur

23) Which of the following statements is not true regarding data collection:

a. often times, in our field, we collect data to help us infer or hypothesize about any number of things including treatments, prevention, occurrences, etc

b. collecting count data may be on one single sample or cohort, due to any number of reasons

c. when data is collected on count data, e call the outcome of that collection, results

. in single group studies, control groups are the standard

24) Which of the following statements is true:

a. comparisons between age-adjusted rates can only be useful if the same standard population is used in the creation of the age-adjusted rates

b. event rates are never seen as something which is important in public health except in epidemiological concerns

c. count data is something that is important when considering data gathered on vampires

d. person-time is often used in epidemiological studies in the veterinary sciences

Dole Pineapple Inc. is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the population standard deviation of the process is .04 ounce. The quality control department took a random sample of 60 cans and found that the arithmetic mean weight was 16.05 ounces. At the 3% level of significance (Step 2), can we conclude that the mean weight is greater than 16 ounces?

Step 1: State the null hypothesis (H0) and the alternate hypothesis (H1). (insert >, >, =,< or <) where appropriate. Ho:  ______ 16 H1:  _______16

Step 2: you select the level of significance, =.03 (Given in problem description)

Step 3: Identify the test statistic (circle ‘t distribution’ or ‘Normal Curve (z)’) use the t distribution or Normal Curve (z)

Step 4: Formulate the decision rule Reject Ho if _______________________

Step 5: Take a sample arrive at a decision

Step 6: Interpret the results (circle ‘Reject’ or ‘Accept’) circle ‘are’ or ‘are not’) Reject or Accept Ho. The cans are or are not being overfilled.

Please show legible work!

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 150 engines and the mean pressure was 4.0 pounds/square inch (psi). Assume the population standard deviation is 0.7 . If the valve was designed to produce a mean pressure of 4.1 psi, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? is there sufficient or not sufficient evidence?

Find the following probabilities.

A.) P(X=5), X FOLLOWING A BINOMIAL DISTRIBUTION, WITH N=50 AND P=.7.

B.) P(X = 5), X following a Uniform distribution on the interval [3,7].

c.) P(X = 5), X following a Normal distribution, with µ = 3, and σ = .7.

(To complete successfully this homework on Stochastic Models, you need to use one of the software tools: Excel, SPSS or Mathematica, to answer the following items, and print out your results directly from the software. )