#3

Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded.

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Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median.  Test the sequence for randomness about the median with a 5% level of significance. What is the value of the sample test statistic R, the number of runs?

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R = 8

R = 9

R = 7

R = 4

R = 6

Cholesterol levels were collected from patients two days after they had a heart attack (Ryan, Joiner & Ryan, Jr, 1985) and are in table #3.3.10.

Find the five-number summary and interquartile range (IQR) (3points), and draw a box-and-whiskers plot with all the components labeled (3 points). Extra Credit (2points): State the shape of the distribution (1 point), upper and lower fence (2 points), and if there are any outliers (1 point).

16.An experiment is rolling a fair dieand then flipping a fair coin.

a.)State and write out all the points in the sample space.

b.)Find the probability of getting a head.  Make sure you state the event space.

c.)Find the probability of getting a 6 or a head.

d.)Find the probability of getting a 3 and a tail.

1) If you were designing a study that would benefit from a narrow range of data points, you would want the input variable to have: a large standard deviation a small mean a small margin of error a small sample size

If) a computer manufacturer needed a supplier that could produce parts that were very precise, what characteristics would be better? narrow confidence interval at low confidence level wide confidence interval with high confidence level narrow confidence interval at high confidence level wide confidence interval with low confidence level

The file P08_06.xlsx contains data on repetitive task times for each of two workers. John has been doing this task for months, whereas Fred has just started. Each time listed is the time (in seconds) to perform a routine task on an assembly line. The times shown are in chronological order. a. Calculate a 95% confidence interval for the standard deviation of times for John. Do the same for Fred. What do these indicate? b. Given that these times are listed chronologically, how useful are the confidence intervals in part a? Specifically, is there any evidence that the variation in times is changing over time for either of the two workers? Please provide it as per the Excel.

Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data: MOE 29.9 33.4 33.6 35.3 35.4 36.2 36.3 36.5 37.7 37.9 38.6 38.8 39.7 41.2 Strength 6.0 7.1 7.3 6.1 8.0 6.6 6.8 7.7 6.7 6.7 7.0 6.5 8.1 8.8 MOE 42.8 42.8 43.4 45.8 45.8 47.0 48.1 49.2 51.8 62.6 69.9 79.6 80.2 Strength 8.3 8.8 8.0 9.6 7.6 7.5 9.7 7.7 7.5 11.6 11.5 11.8 10.9 Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in the data above resulted in ŷ = 7.576, sy hat = 0.178 when x = 40 and ŷ = 9.777, sy hat = 0.251 for x = 60. (a) Explain why sy hat is larger when x = 60 than when x = 40. The closer x is to x, the smaller the value of sy hat. The farther x is from y, the smaller the value of sy hat. The farther x is from x, the smaller the value of sy hat. The closer x is to y, the smaller the value of sy hat. (b) Calculate a confidence interval with a confidence level of 95% for the true average strength of all beams whose modulus of elasticity is 40. (Round your answers to three decimal places.) , MPa (c) Calculate a prediction interval with a prediction level of 95% for the strength of a single beam whose modulus of elasticity is 40. (Round your answers to three decimal places.) , MPa (d) If a 95% CI is calculated for true average strength when modulus of elasticity is 60, what will be the simultaneous confidence level for both this interval and the interval calculated in part (b)? The simultaneous confidence level for these intervals is at least

Does the research problem derive from theory, prior research, or methodological considerations? Explain the rationale for your response and what part of the narrative you used to arrive at the answer.

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 govern-
ment-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.

Determine whether each of the following statements is true or false, and explain why in a few sentences.

1. The mean, median, and mode of a normal distribution are all equal.

2. If the mean, median, and mode of a distribution are all equal, then the distribution must be a normal distribution.

3. If the means of two distributions are equal, then the variance must also be equal.

4. The sample mean is not the same as the population mean.

5. The mode of a distribution is the middle element of the distribution.

6. A large variance indicates that the data are grouped closely together.

Answer the following questions in a few sentences.

7. What is meant by the range of a distribution?

8. How are the variance and the standard deviation of a distribution related? What is measured by the standard deviation?

9. Describe the characteristics of a normal distribution.

10. What is meant by a skewed distribution?

Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (−) in seconds per week.

Data File

a)State the null hypothesis and the alternate hypothesis. State the decision rule for 0.02 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

b)Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

c)Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.02 significance level.

d)Estimate the p-value.

Problem 4.3.8.

In order to guarantee smooth operation, the University has three web- servers. Each can handle the traffic by itself, and the probability that each is not working on a given day is 10%, independently of the other servers. Assuming that the system is up, what is the probability that only one server is functioning?

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 20 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.34 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

lower limit:

upper limit:

margin of error:

(b) What conditions are necessary for your calculations? (Select all that apply.)

uniform distribution of weights

σ is unknown

n is large

normal distribution of weights

σ is known

(c) Interpret your results in the context of this problem.

The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.09 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

You wish to test the following claim ( H a ) at a significance level of α = 0.001 .

H o : μ = 77.2

H a : μ < 77.2

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 16 with mean M = 65.4 and a standard deviation of S D = 15.2 .

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

The p-value is...

less than (or equal to) α or greater than α

This p-value leads to a decision to...

reject the null or accept the null or fail to reject the null

As such, the final conclusion is that...

a . There is sufficient evidence to warrant rejection of the claim that the population mean is less than 77.2.

b . There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 77.2.

c . The sample data support the claim that the population mean is less than 77.2.

d . There is not sufficient sample evidence to support the claim that the population mean is less than 77.2.

Given a standard normal variable, what is the probability Z is greater than 1.25? Round to four decimals and use leading zeros.

A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the 0.02 significance level, is there a relationship between job pressure and age?

State the decision rule. Use 0.02 significance level. (Round your answer to 3 decimal places.)

H₀: Age and pressure are not related.

H₁: Age and pressure are related.

Compute the value of chi-square. (Round your answer to 3 decimal places.)

What is your decision regarding H₀?

The null and alternate hypotheses are:

H₀ : μ_d ≤ 0

H₁ : μ_d > 0

The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of four days last month.

At the 0.100 significance level, can we conclude there are more defects produced on the day shift? Hint: For the calculations, assume the day shift as the first sample.

1. State the decision rule. (Round your answer to 2 decimal places.)

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

3. What is the p-value?

• Between 0.025 and 0.05

• Between 0.001 and 0.005

• Between 0.005 and 0.01

4. What is your decision regarding H₀?

• Reject H₀

• Do not reject H₀

• Given the following data where city MPG is the response variable and weight is the explanatory variable, explain why a regression line would be appropriate to analyze the relationship between these variables:

• Construct the regression line for this data.
• Interpret the meaning of the y-intercept and the slope within this scenario.
• What would you predict the city MPG to be for a car that weighs 3000 pounds?
• If a car that weighs 3000 pounds actually gets 32 MPG, would this be unusual? Calculate the residual and talk about what that value represents