Suppose a client is working on research project for her master’s degree in nursing. She plans to survey registered nurses (RN’s) in Ohio to get their opinions related to the opioid crisis. The target population is all RN’s in Ohio with active registrations. The client has obtained access to a list of all currently registered RN’s in Ohio, along with their contact information and nursing specialty.

Part A. The client plans to use a random number generator to select 800 nurses from this list and contact them by mail, email, and phone, asking them to complete the survey. What type of sampling method is being attempted here? Despite the use of this method, explain how there may still be bias related to which nurses participate.  

Part B. An alternative plan for selecting the nurses might be better if the client also wants to summarize the opinions of nurses separately for various specialty areas, such as Psychiatric, Hospice Care, Post-Op, and Other.   Name the type of sampling method and suggest how the client may go about selecting the sample.

The textbook basically says that the general addition rule is when A and B are two events in a probability experiment. The probability that either one of the events will occur is: P (A or B) = P (A) + P (B) – P (A and B). For example, if you take out a single card from a pack of cards, what is the probability that the card is either an ace or spade? Therefore, P(A) = 4/52, P (B) = 13/52, and P (A and B) = 1/52. P (A or B) = 4/52 + 13/52 – 1/52. P (A or B) = 4/13. Conditional Probability is the probability of one event (A) occurring with a relationship to another event (B). For example, in a sample of 40 vehicles, 18 are red, 6 are trucks, and 2 are both. Suppose that a randomly selected vehicle is red. What is the probability it is a truck? P(truck|red) = P (truck and red) / P (red). P (truck|red) = 2/40 = 18/40 = 2/18 = 1/9 or .11. So, if we must find the probability of an event which will occur given that another event has occurred, we will use conditional probability. If two events are mutually exclusive (no chance of things happening together) and you want to find the probability that an event A or B happens, we will use general addition rule.

"So we could use the general addition rule in the general election (in November elections) and use conditional probability in the primaries?"

According to a recent report, it was found that 50.3% of residents in Cuyahoga County, Ohio are registered to vote. Which of the following is more likely?

Select one:

A) We take a random sample of 100 people from this county and find that the proportion is below 45%

B) We take a random sample of 400 people from this county and find that the proportion is below 45%

C) We take a random sample of 1000 people from this county and find that the proportion is below 45%

D) We take a random sample of 10000 people from this county and find that the proportion is below 45%

E) We have no basis for predicting which is more likely to have a proportion below 45%.

1. The following probability distribution represents the number of people living in a Household (X), and the probability of occurrence (P(X)). Compute the Expected Value (mean), the Variance and the Standard Deviation for this random variable. Show Your Calculations for the Mean.

    X      1         2        3          4        5               

P(X)    .33      .29      .27        .07       .04     

2. Use the binomial formula to compute the probability of a student getting 8 correct answers on a 10 question Quiz, if the probability of answering any one question correctly is 0.64. SHOW YOUR WORK.

3. Submit your answers to the following binomial questions. You may use the appendix table B #5 to answer parts (a) and (b). According to a government study, 20% of all children live in a household that has an income below the poverty level. If a random sample of 15 children is selected:

a) what is the probability that 6 or more live in poverty?

b) what is the probability that 5 live in poverty?

c) what is the expected number (mean) that live in poverty?

At a call center, calls come in at an average rate of four calls per minute. Assume that the time elapsed from one call to the next has the exponential distribution, and that the times between calls are independent.

a. Find the average time between two successive calls.

b. Find the probability that after a call is received, the next call occurs in less than ten seconds.

c. Find the probability that less than five calls occur within a minute.

d. Find the probability that more than 40 calls occur in an eight-minute period.

e. Find a 95% confidence interval for the number of calls in a minute.

The Relationship Between State Agencies and Nonprofit Organizations Introduction The relationship between government agencies and nonprofit organizations is the focus of increasing attention within the public administration community. Practitioners recognize that the organization of public services relies to a substantial degree upon what we have come to call third-party government (Salamon, 1981). Nongovernmental actors not only deliver government-funded services but also actively participate throughout the policy process. Often the third-party is a nonprofit organization. In the last decade or so, researchers from a variety of disciplines have examined this evolutionary development more closely (Kramer, 1981; Salamon and Abramson, 1982; Salamon, 1987; Gronbjerg, 1987; Ostrander, Langton, and Van Til, 1987; Lipsky and Smith, 1989-90; Wolch, 1990; Provan and Milward, 1990). A 1989 National Academy of Public Administration report, Privatization: The Challenge to Public Management, urged that public administrators and policymakers in general acknowledge the significant management challenges posed by government programs that involve such "tools of government action" as contracting out, loan guarantees, government sponsored enterprises, and vouchers (Salamon, 1989b). Within this context of extensive sharing of responsibility between governmental and nongovernmental actors for operating public programs, the government/nonprofit relationship is widely acknowledged as a critical element. The shrinking capacity of public organizations, increasing demand for services, and continuing trend toward decentralized program delivery underscore its importance. At the same time, an understanding of the precise character of the state/voluntary sector relationship and the degree of interdependence between public agencies and nonprofit organizations requires additional empirical investigation. Research findings reported here describe that relationship in terms of the dependence of public agencies and nonprofit organizations on each other for resources and their resulting interdependence. The framework laid out in this study emerged from a synthesis of three sources: (1) the perspectives of organization theory, especially power/dependence and resource dependence, and bureaucratic politics; (2) a series of exploratory model refinement interviews with four public-sector and five nonprofit- sector participants in an earlier policy study (Dawes and Saidel, 1988); and (3) a field pretest in June-July 1989, with 20 state agency and 20 nonprofit administrators from four service areas. Emerson's (1962) theory of reciprocal power-dependence relations provided the building blocks for the framework used in this research. He reasoned that the power of A over B is equal to, and based upon, the dependence of B upon A. Recognizing the reciprocity of social relations, we can represent a power-dependence relation as a pair of equations: Pab = Dba Pba = Dab (Emerson, 1962, p. 33). For the purposes of this study, if a becomes s for state agencies and b becomes n for nonprofit organizations, the equations can be read as follows: The power of state agencies over nonprofit organizations equals the dependence of nonprofit organizations on state agencies for resources (Psn = Dns). The power of nonprofit organizations over state agencies equals the dependence of state agencies on nonprofit organizations for resources (Pns = Dsn). The use of Dsn and Dns yields two measures of resource dependence that, taken together, delineate a current picture of resource interdependence between state and nonprofit organizations. What resources, common across service areas, are exchanged between state government bureaucracies and public benefit nonprofit organizations? Resources that flow from state agencies to nonprofit organizations are: revenues; information, including expertise and technical assistance; political support and legitimacy, in the sense of external validation (Galaskiewicz, 1985); and access to the nonlegislative policy process (Rourke, 1984). Nonprofit organizations supply their service-delivery capacity, information, political support, and legitimacy to state agencies. Nonprofit organization service-delivery capacity was documented as a substantial resource to government in the Urban Institute Nonprofit Sector Project finding that "nonprofit organizations actually deliver a larger share of the services government finances than do government agencies themselves" (Salamon, 1987, p. 30). Three resource dependence criteria or dimensions of dependence (Bacharach and Lawler, 1981) can be specified: (1) the importance of the resource; (2) the availability of alternatives; and (3) the ability to compel provision of the resource. The importance, or essentiality of a resource to an organization, consists of the organization's need for the resource in order to function, to operate, or to deliver programs or services (Levine and White, 1961; Emerson, 1962; Blau, 1964; Jacobs, 1974; Thompson, 1967; Cook, 1977; Pfeffer and Salancik, 1978; Brudney, 1978; Aldrich, 1979; Provan, Beyer, and Kruytbosch, 1980; Provan and Skinner, 1989). The importance dimension incorporates the elements of substitutability and criticality or the organization's ability to forego the resource and still continue operating (Jacobs, 1974; Pfeffer and Salancik, 1978; Aldrich, 1979). The availability of the same resource from another supplier is widely acknowledged as a dimension of dependence (Levine and White, 1961; Emerson, 1962; Blau, 1964; Thompson, 1967; Jacobs, 1974; Cook, 1977; Pfeffer and Salancik, 1978; Brudney, 1978; Provan and Skinner, 1989). Cook's explanation is representative: "To the extent that alternative sources are available to an organization in an exchange network, dependence is less..." (1977, p. 66). Insofar as organization A can compel, pressure, or force organization B to provide needed resources, A is less dependent on B. In contrast to the availability of alternatives, this dimension appears much less frequently in the literature (Blau, 1964; Aldrich, 1979; Provan, Beyer, and Kruytbosch, 1980). In the context of third-party government research, the ability to compel provision of a resource includes statutory and regulatory sanctions as well as the use of less formal kinds of pressure to force resource provision. This expanded scope is appropriate to the complex political environment within which inter-organizational resource exchanges occur across sectors. In order to determine the degree of reciprocal dependence, it is important to examine both state and non-profit administrators with respect to the level of dependence each group perceives both state and non-profits have on each other. While the literature has provided a framework for the factors that need investigation, it has not provided any evidence of actual differences in dependence (or the perception of dependence), either generally or in the case of specific service areas. The present study examined four key variables. The first was the general dependence of nonprofit organizations on states (the importance of the resource obtained from the state, the availability of the resource from alternative sources, and the ability to compel the provision of the resource from the state). The second was the general dependence of the state on nonprofit organizations (the importance of the resource obtained from the nonprofit organization, the availability of the resource from alternative sources, and the ability to compel the provision of the resource from the nonprofit organizations). These were derived from the work of Bacharach and Lawler (1981). The third was dependence of the state on the non-profit organizations by service sector (arts, health, developmental disabilities, and human services). The fourth was dependence of nonprofit organizations on the state by service sector (arts, health, developmental disabilities, and human services). The following hypotheses characterized the specific expectations of the study: [Itemize All Hypotheses Here] Method Sample The population of interest in this study was 1) nonprofit organizations in the State of New York in one of the designated service areas, and 2) divisions within the state system in each of the same service areas. An explanation of the study was sent to each sector (nonprofit and state) requesting responses from interested parties. The final sample of 80 nonprofit organizations consisted of a random sample of 20 organizations in each of the four service areas – arts, health, developmental disabilities, and human service areas – from those who indicated interest. The sample from the state was obtained by randomly selecting 20 persons from the same four service sectors from those who responded with interest. Tables 1 and 2, below, present the principle descriptive categorical and continuous information, respectively, for the two final groups: [Insert Table 1 Here] [Insert Table 2 Here] Measures To measure reciprocal resource dependence of state agencies and nonprofit organizations, 14 Likert-type scales were constructed with a number of items to which the respondent indicated intensity of agreement or disagreement on a six-point scale. Response categories were strongly disagree, generally disagree, disagree a little, agree a little, generally agree, strongly agree. The conceptual anchors of each scale were (1) independence and (6) dependence. That is, higher scores represented greater dependence in the area being assessed. Three scales (importance, alternative availability, and pressure) measured the dependence of state agencies on nonprofit organizations for resources. Three parallel scales measured the same dimensions for resource dependence in the other direction, that is, the dependence of nonprofit organizations on state agencies for resources. Items were predominantly attitudinal; some were behavioral. The following items are samples from the importance, alternative availability, and pressure scales, respectively. S1. State agencies often use ideas from nonprofit organizations to formulate policy recommendations. N1. Nonprofit organizations often use ideas from state agencies lO formulate policy recommendations. S2.There are certainly other supporters of agency interests as valuable as nonprofit organizations. N2. There are certainly other supporters of nonprofit organizations' interests as valuable as state agencies. S3.Agencies are in no position to force nonprofit organizations to implement their programs. N3. Nonprofit organizations are in no position to force agencies to fund their programs. Scale scores were the average of the item scores. Table 3 reports reliability results for the six scales. Alpha reliability coefficients are listed in bold-face type. Discriminant validity may be measured by the inter-scale correlation coefficients shown on the diagonal in that table. Table 3: Reliabilities of State and Nonprofit Scales Scale Reliability State Importance .67 State Alternative Availability .73 State Pressure .63 Nonprofit Importance .70 Nonprofit Alternative Availability .70 Nonprofit Pressure .75 The remaining eight scales were divided, four each for state departments and non-profit agencies, into individual service areas. These were arts, health, developmental disabilities, and human services. The first set of four examined dependence of the state departments on nonprofit agencies in the four areas; the second set of four scales assessed the dependence of nonprofits on state agencies in the same four areas. The average of the three individual scale scores measuring state agency dependence on nonprofit agencies became Dsn in the model. The average of the three individual scale scores measuring nonprofit agency dependence on state agencies became Dns. These reciprocal resource flows, understood together, became the basis for a g e n e r a l model of resource dependence between sectors. Design The design of the study was [Enter the Study Design Here]. The particular strengths of this design are [Enter the Design Strengths Here]. The design is weak in the areas of [Enter the Design Weaknesses Here]. Procedure The total number of study participants was 153: 80 nonprofit and 73 state agency managers. Public-sector respondents were 20 people, including commissioners, from each of the 4 state agencies and executive directors from 20 nonprofit organizations in each of the service areas. Of the 80 nonprofit agency respondents, 14 were top-level managers other than the executive director. All nonprofit and some state agency respondents participated in two-part, on-site interviews, including a self-administered survey completed immediately and an interview with demographic and open-ended questions. State agency commissioners designated two additional executive administrators for the research interview, and they, in turn, identified 17 other managers to receive a mailed survey.

1. a) What is/are the independent variable(s) in your study? (5 points)

PADM 580

Assignment 1

b) What is/are the dependent variables in your study? (5 points)

a) Average talk time between charges of a cell phone is advertised as 4.6 hours. Assume that talk time is normally distributed with a standard deviation of 0.6 hours.

Find the probability that talk time between charges for a randomly selected cell phone is either more than 5.7 hours or below 2.8 hours. (If you use the z table, round the "z" value to 2 decimal places. Round your final answer to 4 decimal places. Do NOT express as a percentage.)

b) Average talk time between charges of a cell phone is advertised as 4.6 hours. Assume that talk time is normally distributed with a standard deviation of 0.6 hours.

Twenty-nine percent of the time, talk time between charges is below a particular value. What is this value? (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

c) Average talk time between charges of a cell phone is advertised as 4.6 hours. Assume that talk time is normally distributed with a standard deviation of 0.6 hours.

Find the probability that talk time between charges for a randomly selected cell phone is below 3.7 hours. (If you use the z table, round  "z" value to 2 decimal places. Round your final answer to 4 decimal places. Do NOT express as a percentage.)

Please refer to the question from textbook Stats: Data and Models 4th Edition, Chapter 4, Exercises, Section 4.5 Chapter exercises #22 Camp Sites, part (b): How many parks would you classify as outliers ? Explain

Discuss an example of applying probability to investigating burglaries . What are some ways you could measure or express that probability using the Basic Law of Probability.

Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, let ? be the number of patients in the sample that actually have the flu.

Explain why ? can be treated as a binomial random variable.

• Identify ? (the number of trials):                   ? = ___________

• Specify (in words) which event would be defined as a “success”

• Explain why the trials may be considered independent:

• Give the value of ? (the probability of success): ? = ___________

b) On average, for every 25 patients calling in, how many do you expect to actually have the flu?

c) What is the probability that exactly 5 of the 25 patients actually have the flu?

d) What is the probability that at least two of the 25 patients actually have the flu?

Suppose that you want to create a portfolio that consists of a corporate bond​ fund, X, and a common stock​ fund, Y. For a​ $1,000 investment, the expected return for X is $75 and the expected return for Y is $ 90 The variance for X is 1,725 and the variance for Y is 12,225. The covariance of X and Y is 4,583.

a. The portfolio risk is ​$

b. Compute the portfolio expected return and portfolio risk if you put $ 500 in each fund.The portfolio expected return is

​(Type an integer or a​ decimal.)

The portfolio risk is

​(Round to two decimal places as​ needed.)

c. Compute the portfolio expected return and portfolio risk if you put $600 in the corporate bond fund and $400 in the common stock fund.The portfolio expected return is

​(Type an integer or a​ decimal.)

The portfolio risk is

​(Round to two decimal places as​ needed.)

1). If a couple has two children, what is the probability that they are both girls assuming that the older one is a girl?

2). Suppose that we have two dice, the first one being a regular die, and the second weighted so that half the time it rolls a 1, and half the time it rolls a 2 (it never rolls anything else). If we choose one of these dice at random, and roll a 1, what’s the probability that it is the regular die?

A study of 90 workers following a new pre-work stretching exercise program was conducted. One of the variables measured over the 4-week study was the increase in number of minutes worked in an hour. A previous program had produced an average increase of µ = 2 mins per hour. The company wants to evaluate whether the new program had increased µ in comparison
with the previous program. The study data yielded x̅= 2.17 and s = 1.05.

a. At the 5 percent level of significance, compare the new program to the previous one.

b. What is the probability of making a Type II error if the actual value of µ is 2.1 min per
hour?

If Z is a bernoulli random variable such that point (X,Y) falls within unit circle with center (0,0) and given that X & Y are independent uniform random variables with range [-1,1] and X^2 + Y^2 <1. Find the expectation E(Z) and Std. Deviation of Z.