Problem #4

PERT Analysis: Consider the project with the following estimates for activity times and precedence relationships (be sure to use the triple time estimate). All times are in days:

What is the expected duration of the project?

If the deadline of the project is 26 days, what is the probability of finishing the project on time?

A cooking article reported that cooking a quality meal takes time; in fact, the article states that it takes longer than 45.0 minutes. Suppose a study is conducted to test the validity of this statement at a 95.00% confidence interval/level. A sample of 18 people is selected, and the length of time to put a meal on the table is listed: 45.20 40.70 41.10 49.10 30.90 45.20 55.30 52.10 45.40 55.10 38.80 43.10 39.20 58.60 49.80 43.20 47.90 46.60 What will be the hypothesis in this study? What will be the area of rejection in this study using p critical value? Create the statement of rejection or not-rejection based upon the p value and the p critical value What will be the conclusion of this study?

Discuss the uses of data mining

1. Healthcare
2. Finance
3. Retail and e-commerce

For any confidence interval make sure that you interpret the interval in context, in addition to using it for inference.

A survey is given to 300 random SCSU students to determine their opinion of being a “Tobacco Free Campus.” Of the 300 students surveyed, 228 were in favor a tobacco free campus.

1. Find a 95% confidence interval for the proportion of all SCSU students in favor of a tobacco free campus.
2. Interpret the interval in part a.
3. Find the error bound of the interval in part a.
4. The Dean claims that at least 70% of all students are in favor of a tobacco free campus. Can you support the Dean’s claim at the 95% confidence level? Justify!

An economist is interested in whether the level of the minimum wage affects employment. In order to study this issue they got data from a random sample of 322 New Jersey fast food restaurants before and after an increase in the NJ minimum wage from $4.25 to $5.05 per hour. The change in full time equivalent employees per restaurant in the sample before and after the increase was 0.80 with a variance of 77.5. Must not be done using excel.

1. Test whether this suggests the increase in the minimum wage had an effect on employment.
2. What statistical errors might have been made?
3. Why might this not answer the question?

A 1980 study was conducted whose purpose was to compare the indoor air quality in offices
where smoking was permitted with that in offices where smoking was not permitted. Measurements were made
of carbon monoxide (CO) at 1:20 p.m. in 36 work areas where smoking was permitted and 36 work areas where
smoking was not permitted. In the sample where smoking was permitted, the mean CO = 11.6 parts per million
(ppm) and the standard deviation CO = 7.3 ppm. In the sample where smoking was not permitted, the mean CO
= 6.9 ppm and the standard deviation CO = 2.7 ppm. Test for whether or not the mean CO is significantly (α =
0.05) different in the two types of working environments.
(a) What is the null hypothesis for this problem? What is the alternative hypothesis?
(b) For this problem, would you perform a one- or two-tailed test? Explain how you reached that decision.
(c) Determine which procedure (you have learned five situations) is the appropriate statistical test to use, with
a clear explanation for your choice.
(d) Using your calculator, test the null hypothesis and present your results. Show all your work.
(e) Using statistical language (“statistic-ese”), state your conclusion and your reasoning for reaching this
conclusion. Then restate your conclusion, this time in English instead of “statistic-ese,” without including
statistical symbols or the term hypothesis. (What is the answer to the researcher’s question?)
(f) State, based on your conclusion, whether you may have committed a Type I error or a Type II error, and
what that means.

In one of the studies, it was found that, in a random sample of 261 married persons, 135 were smokers while in a sample of 239 non-married persons there were 131 smokers.

a. Find a 90% confidence interval for the true difference in proportion of smokers among the married and non-married populations.

b. Based on the above interval, can one conclude that there is a significant difference between the proportions of smokers in the two populations? Justify your answer

c. Do a formal hypothesis testing to test whether the two populations proportions are significantly different. Use ? = 0.10 and a p-value method. Set up the appropriate null and alternative hypotheses. Is the conclusion same as the one in part(b)?

A group of n = 25 students was selected at random for studies related to the amount of time they spent for exam preparations. Educators assume that individual records are normally distributed with entirely unknown parameters (μ, σ). Sample summaries (in minutes per week) were obtained as

Sample Mean =X =90 and Sample SD =s=20 For hypothesis testing, set significance level = α = 0.01̄

1. To test whether μ < 100, what critical value (or values) are you going to use?

2. Formulate rejection rule that explains whether you are rejecting the null hypothesis or not

3. Evaluate the test statistic

4. State your decision in the form:
   Yes, we have enough evidence to reject the null hypothesis or No, we do not have evidence to reject the null hypothesis

Weatherwise is a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height of μ = 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of 35 waves showed an average wave height of x = 17.7 feet. Previous studies of severe storms indicate that σ = 3.5 feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Use α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ > 16.4 ft; H₁: μ = 16.4 ftH₀: μ = 16.4 ft; H₁: μ > 16.4 ft    H₀: μ = 16.4 ft; H₁: μ < 16.4 ftH₀: μ < 16.4 ft; H₁: μ = 16.4 ftH₀: μ = 16.4 ft; H₁: μ ≠ 16.4 ft

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since the sample size is large and σ is known.The standard normal, since the sample size is large and σ is known.    The standard normal, since the sample size is large and σ is unknown.The Student's t, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to two decimal places.)


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


Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Sansuit Investments is deciding on future investments for the coming two years and is considering four bonds. The investment details for the next two years are given in the table below.

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The net worth of these four bonds at maturity is $60,000, $40,000, $25,500, and $18,000, respectively. The firm plans to invest $35,000 and $62,000 in Year 1 and Year 2, respectively. Develop ( write all the constraints) and solve a binary integer programming model with SOLVER for maximizing the net worth. Give your answer clearly

A shipping freighter has space for two more shipping containers, but the combined weight cannot go over 20 tons. Four shipping containers are being considered. The following table provides details on the weight (in tons) and value of the contents of each container.

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Develop a binary integer model ( write all the constraints) that will determine the two containers, solve by SOLVER that will maximize the value of the shipment.

A beverage can manufacturer makes three sizes of soft drink cans—Small, Medium and Large. Production is limited by machine availability, with a combined maximum of 105 production hours per day, and the daily supply of metal, no more than 200 kg per day. The following table provides the details of the input needed to manufacture one batch of 100 cans for each size.

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a. Develop a linear programming model by identifying the variables, writing the objective function

b. Write all necessary constraints

c. Find the maximized profit and determine how many batches of each can size should be produced.

In a preliminary study of 45 customers, we ask how much they would pay for an upgrade to their water filtration system; for this sample, the average price is 35 with a variance of 400. How many customers would we need to contact in order to be 80% confident that the estimated price will be within 2 euro of the true price?