1. The distribution of body sizes (in g) of wild mosquitoes breeding in the Back Bay Fens was sampled. Fifteen male mosquitoes were weighed, with the following results. Are they larger than the typical male (1.3 g)?

1.60, 1.61, 1.07, 1.34, 1.45, 1.43, 1.16, 2.11, 1.77, 1.08, 1.79, 1.07, 1.59, 2.07, 0.85

1. What is the appropriate test to use for these data? Justify your answer.
2. Test the hypothesis that these mosquitos are significantly larger than the typical male of the species. Let a = 0.05.
3. What is the 95% confidence interval for the mean based on this sample?

The age of Facebook users is normally distributed. The average age of a user on Facebook is 40.5 with a standard deviation of 10. 1. What is the probability that a single randomly selected person that is on Facebook is less than 20 years of​ age? (round to four​ decimals) nothing 2. What is the probability that a sample of 15 Facebook useres is between 30 and 40 years of​ age?

1.  The gestation period (length of pregnancy) for male babies born in New York is normally distributed with a mean of 39.4 weeks and a standard deviation of 2.3 weeks.

(a)  What percent of mothers of male babies are pregnant for less than 35 weeks?

(b)  What percent of mothers of male babies are pregnant for between 35 and 40 weeks?

3. What percent of mothers of male babies are pregnant for more than 40 weeks?
4.   Suppose a sailor had shore leave 46 weeks ago and his wife is delivering a baby today.  What should the sailor say to his wife when he gets home?

Determine the Appropriate Analysis For each of the following scenarios, identify the appropriate analysis.

2. A guidance counselor at a high school wants to be best informed about the universities and colleges that students prefer most frequently. He glances at the institutions attended by last year’s graduates and notes that the three closet colleges appear to have about equal appeal. To test this assumption, he begins asking students who are planning on postsecondary schooling where they will apply. His data are as follows:

The technical institute: 22

The community college: 18

The comprehensive university: 12

Recall the lifetime (in months) of a battery is modeled by a random variable X that has pdf fθ(x)=Kθx1(x>0)where K=ln(1/θ) for an unknown parameter θ∈(0,1) .

Assume instead that we cannot actually observe the lifetime of the batteries. Instead, we only observe if the battery is still working after τ months for some known τ to be chosen later (this is called censored data ).

Let Y1,…,Yn be our observations where Yi=1(Xi>τ) indicates that the i th battery is still working after τ months. Our goal is to estimate θ∈(0,1) (the parameter for the pdf of X ) based on this new data.

The quantity n−−√(θ~−θ) converges in distribution to N(0,σ2~) . Find the asymptotic variance σ2~ . σ2~=

Company A is trying to sell its website to Company B. As part of the sale, Company A claims that the average user of their site stays on the site for 10 minutes. To test this claim Company B collects the times (in minutes) below for a sample of 10 users. Assume normality.

Time 1.6

25.9

7

23.3

7.3

8.8

18.5

8.6

10.8

12

Construct a 95% confidence interval for the true mean time spent on the web site.

a) What is the lower limit of the 95% interval? Give your answer to three decimal places. Enter 0 if your lower limit is less than 0.

b) What is the upper limit of the 95% interval? Give your answer to three decimal places.

c) Based on this data, do you believe the claim made by Company A?

Yes because 10 is not inside the interval.

No because 10 is not inside the interval.

Yes because 10 is inside the interval.

No because 10 is inside the interval.

d) Which of the following assumptions should be checked before constructing the above confidence interval?

the data need to have small variance

the data need to follow a t distribution

the data need to be skewed

the data need to follow a normal distribution

List and explain the t-test assumptions.

Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer it takes the plane to unload and load passengers. One regional airline is considering changing its policy to allow only one carry-on per passenger. Before doing so, the airline decided to collect some data. Specifically, a random sample of 1000 passengers was selected. Researchers observed the passengers and noted the number of bags each person carried on the plane. Out of the 1000 passengers, 340 had more than one bag.

1. Based on this sample, develop and interpret a 99% confidence interval estimate for the proportion of the traveling population that would have been impacted had the “one-bag” limit been in effect. Discuss your result.

2. The domestic version of Boeing’s 757 has a capacity for 220 passengers. Determine an interval estimate of the number of passengers you would expect to board the plane with more than one carry-on. Assume the plane is at its passenger capacity.

a. What is hypothesis testing in statistics? Discuss

b. Does Type I error being considered more serious than Type II error? Explain

c. What is the p-value of a test? Give an example

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.77.

(c) How large a sample size is necessary if the width of the 95% interval is to be 0.42? (Round your answer up to the nearest whole number.)

(d) What sample size is necessary to estimate true average porosity to within 0.23 with 99% confidence? (Round your answer up to the nearest whole number.)

1) A student learns that on his most recent exam in environmental science, the sample mean was 67.08 with a standard deviation of 16.81. He scored a 75. If we assume that this is a population, and is normally distributed, what proportion of students in the class scored worse than this student? Enter your answer to four decimal places.

This chapter and assignment further explore standards for interoperability. The HIMSS definition of interoperability states, “The ability of two or more systems or components to exchange information and to use the information that has been exchanged.” HIM professionals often are the subject matter experts when a question about standards arises and need to help guide the IT analysts and workers at their organization. An example from a recent conference I attended: “The IT professionals will say, we can make that happen, but it is the HIM professionals that have to caution them to slow down and think through the consequences, i.e., explain to the IT professionals why it may not be logical or practical to proceed.”

Instructions

Please answer the following questions on the discussion board and then respond to two of your classmates’ postings. Responses should be approximately 250 words for this assignment. A rubric is included for guidance on all discussion board postings. NOTE In order to see the postings your classmates have made, you must first post your response.

1. Identify what standards and regulations must be considered when promoting interoperability (organization-to-organization versus a merger and acquisition).
2. Are there some standards that are imperative? Are there some that are priorities over others?
3. Are there any standards are that are not necessary?

A shop is selling stationery through two shops in town, and their website allows online orders. They receive online orders from two of their regular customers, each requiring glossy A3 printing paper. Customer X needs 40 boxes, whereas customer Y needs 60 boxes.

The shop in the north side of town has 85 boxes of glossy A3 paper in stock, whereas their south side shop has 55 boxes in stock. Delivery costs per box are as follows: $0.55 from the north shop to customer X, $0.65 from the north shop to customer Y, $0.45 from the south shop to customer X, and $0.60 from the south shop to customer Y.

Solve using simplex method and draw a clear graphical representation of the problem.

a) Develop the optimization problem to minimize the total delivery costs for this shop.

b) Identify how many boxes of glossy A3 paper need to be shipped from which shop to the two customers. Show your calculations in detail, along with a graphical interpretation of the problem and its solution.

Remember that there is a common notation for the number of levels in a factor and the total number of scores in the entire study. Using these symbols, what are the formulas for each of the following:
dftotal= syntax error

dfwithin=
(also known as the denominator degrees of freedom or the error term degrees of freedom)

dfbetween=
(also know as the numerator degrees of freedom or the treatment degrees of freedom)

6.124a During the National Football League’s 2014 AFC championship game, officials measured the air pressure on 11 of the game footballs being used by the New England Patriots. They found that the balls had an average air pressure of 11.1 psi, with a standard deviation of 0.40 psi.

1. Assuming this is a representative sample of all footballs used by the Patriots in the 2014 season, perform the appropriate test to determine if the average air pressure in footballs used by the Patriots was significantly less than the allowable limit of 12.5 psi. There is no extreme skewness or outliers in the data, so it is appropriate to use the t-distribution.