The data show the population (in thousands) for a recent year of a sample of cities in South Carolina.

Source: U.S. Census Bureau.

Find the data value that corresponds to each percentile.

a. 40th percentile

b. 75th percentile

c. 90th percentile

d. 30th percentile

Using the same data, find the percentile corresponding to the given data value.

e. 27

f. 40

g. 58

h. 67

A number of minor automobile accidents occur at various high-risk intersections in York county despite the traffic lights. The traffic department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and lights at those intersections were modified. The number of minor accidents during a six-months periods before and after the modifications were

At the .01 significance level, it is reasonable to conclude that the modifications reduced the number of traffic accidents?

Assume n independent observations, denoted Xi, (i=1,....n), are taken from a distribution with a mean of E(X)=μ and variance V(X) =σ2. Prove that the mean of the n observations has an expected value of E(X)=μ and a variance of V(X) =σ2/n. Use the appropriate E and V rules in your answer. What happens as n becomes large? What does this tell you about the quality of the sample mean as an estimate of μ as the sample size increases?

Triangulation is the process of examining data and other factors from different perspectives to establish a study’s validity.

What is your interpretation of validity in qualitative research? How should researchers use triangulation to establish validity in your qualitative concept paper?

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 13 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 = 0.36 gram. When finding an 80% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) zc = (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.) σ is known σ is unknown uniform distribution of weights normal distribution of weights n is large (c) Interpret your results in the context of this problem. 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. The probability to the true average weight of Allen's hummingbirds is equal to the sample mean. 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) Which equation is used to find the sample size n for estimating μ when σ is known? n = zσ E σ n = zσ σ E 2 n = zσ E σ 2 n = zσ σ E Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.10 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) hummingbirds

Here are summary statistics for randomly selected weights of newborn girls: n = 192, X=26.5 hg, S= 7.1 Construct a confidence interval estimate of the mean. Use a 99% confidence level. Are these results very different from the confidence interval 24.4 hg < U < 28.0 hg with only 19 sample values, X= 26.2 hg, and S= 2.7 Hg?

What is the confidence interval for the population mean ? ? ___hg < U< ___ hg

8. The following data are for a series of external standards of Cd²⁺ buffered to a pH of 4.6.¹⁴

[Cd²⁺] (nM) 15.4 30.4 44.9 59.0 72.7 86.0

S_spike (nA)    4.8 11.4 18.2    26.6    32.3    37.7

(a) Use a linear regression analysis to determine the equation for the calibration curve and report confidence intervals for the slope and the y-intercept.

(b) Construct a plot of the residuals and comment on their significance.

At a pH of 3.7 the following data were recorded for the same set of external standards.

[Cd²⁺] (nM) 15.4 30.4 44.9 59.0 72.7 86.0

S_spike (nA) 15.0    42.7 58.5 77.0 101    118

(c) How much more or less sensitive is this method at the lower pH?

(d) A single sample is buffered to a pH of 3.7 and analyzed for cadmium, yielding a signal of 66.3 nA. Report the concentration of Cd²⁺ in the sample and its 95% confidence interval.

An analysis is conducted to compare mean time to pain relief (measured in minutes) under four competing treatment regimens. Summary statistics on the four treatments are shown below. The ANOVA table presented below is not completed.

a. What is the within group (error) degrees of freedom value (df₂)?

b. Based on the data and ANOVA table provided in Q44, compute the MSE. (round to 2 decimal places)

c.  Based on the data and ANOVA table provided in Q44, compute the F test statistic. (round to 2 decimal places)

d.  What is the critical value for the hypothesis test you performed in Q44-Q46? (2 decimal places)

A small pilot study is conducted to investigate the effect of a nutritional supplement on total body weight. Six participants agree to take the nutritional supplement. To assess its effect on body weight, weights are measured before starting the supplementation and then after 6 weeks. The data are shown below. Is there a significant increase in body weight following supplementation? Run the test at a 5% level of significance, assuming the outcome is normally distributed. (enter 1 for “yes”, and 0 for “no”)

ath & Music (Raw Data, Software Required):
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

Construct a truth table for the statement [q∨(~r∧p)]→~p.

Complete the truth table below by filling in the blanks. (T or F)

A researcher wants to assess association between high blood pressure prevalence and the amounts of processed foods. If the level of education is associated with both amounts of processed food and high blood pressure, is education a confounder or effect modifier?

Mini-Case Study 3: Debt Spending

A study found that American consumers are making average monthly debt payments of $983 (Experian.com- November 11th, 2010). However, the study of 26 metropolitan areas reveals quite a bit of variation in debt payments, depending on where consumers live. For example, the Washington, DC, residents pay the most ($1,285 per month), while Pittsburghers pay the least ($763 per month). Madelyn Davis, an economist at a large bank, believes that income differences between cities are the primary reason for the disparate debt payments. For example, the Washington, DC, area’s high incomes have likely contributed to its placement at the top of the list. Madelyn also wonders about the likely effect of unemployment on consumer debt payments. She wonders areas with higher unemployment rates will leave consumers struggling to pay their bills and thus lower debt payments. On the other hand, higher unemployment rates may reduce consumer debt payments, as consumers forgo making major purchases such as homes and cars. In order to analyze the relationship between income, the unemployment rate, and consumer debt payments, Madelyn gathers data from the same 26 metropolitan areas used in the debt payment study. Specifically, she collects each area’s 2010-2011 median household income as well as the monthly unemployment rate and average consumer debt for August 2010.

Madelyn asks for your group’s help to:

1. Use the ‘Data Analysis Toolpack’ to fit a regression. Be sure to include all steps including interpreting the model. Be thorough in describing your process. (20 points)

2. Use your final equation to predict the average debt payment of a metropolitan area whose median income is $41,203 and whose unemployment rate is 8.04%. (3 points)

3. Does the intercept have meaning? (3 points)

The Office of the Superintendent of Bankruptcy of Canada (OSBC) is developing a new index to measure the vulnerability of firms in the new technology industry. The index is a ratio of current assets to current liabilities adjusted for various factors specific to this industry. The OSBC wants to compare the index among healthy and failed firms for validation purposes. They expect that failed firms should have a lower index than the healthy ones. Based on a Canadian business registry, they draw a random sample of 68 firms still in operations and another random sample of 33 firms which failed in the last 3 years.

Healthy   Failed
1.50   0.82
2.08   0.05
2.23   1.68
0.89   0.91
1.91   1.16
1.20   0.42
1.95   0.88
2.73   1.11
1.62   2.03
1.71   0.92
1.03   0.73
1.96   0.89
0.10   0.83
1.43   0.99
2.50   0.52
0.23   1.32
1.67   0.48
2.17   1.10
2.61   0.19
1.56   0.51
1.76   0.26
1.02   0.88
1.80   1.31
1.81   0.90
1.76   0.62
0.68   1.45
2.02   1.17
1.20   0.93
1.87   0.75
2.61   0.13
1.11   1.12
2.73   1.15
2.22   0.71
2.50  
0.67  
1.14  
3.15  
1.44  
2.16  
1.21  
3.05  
0.95  
0.90  
2.80  
1.55  
2.44  
1.84  
1.24  
1.39  
1.80  
2.05  
1.52  
0.96  
2.12  
1.85  
1.69  
2.30  
2.21  
2.03  
1.64  
1.87  
1.06  
1.93  
2.25  
1.42  
0.96  
1.64  
2.21  

a) Use Minitab or other appropriate software to produce boxplots of the index values for the two groups of firms and comment on their distribution. 2

b) Use an appropriate statistical test to determine, at the 1% significance level, whether the data provide evidence of a higher average index for the healthy firms. Make sure you provide your manual calculations using the critical value approach.

c) Calculate manually a 99% one-sided confidence interval for the difference in the average index of healthy and failed firms and compare your results with b) above.

d) Use Minitab or other appropriate software to perform the calculations in b) and c) above and comment on any differences.