We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here (data481.dat) is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality.

(a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?

(c) State carefully what the slope tells you about the relationship between wages and length of service.

(d) Give a 95% confidence interval for the slope.
( _______ ,________ )

Answer all questions please

thank you

worker  wages   los     size
1       46.2755 117     Large
2       47.091  80      Small
3       47.8511 16      Small
4       59.5874 43      Small
5       38.4633 120     Large
6       71.1974 201     Small
7       38.8608 95      Large
8       50.6896 80      Large
9       56.9853 22      Large
10      45.4327 150     Small
11      58.0542 54      Large
12      55.6568 47      Small
13      54.9525 22      Small
14      55.8058 37      Large
15      53.6052 173     Large
16      60.9977 19      Large
17      49.5071 106     Large
18      55.4894 168     Small
19      45.1547 31      Large
20      51.0904 90      Large
21      82.706  53      Large
22      40.0094 85      Small
23      39.7198 78      Large
24      40.4793 130     Small
25      55.226  23      Large
26      67.7592 70      Small
27      37.2332 154     Small
28      62.0567 59      Large
29      48.24   54      Large
30      38.2374 57      Large
31      49.9539 75      Small
32      49.698  95      Large
33      42.1205 131     Large
34      65.2506 42      Small
35      43.5929 41      Large
36      40.8412 62      Large
37      44.0662 147     Large
38      79.6358 33      Small
39      37.1909 56      Large
40      37.3583 172     Small
41      52.1068 108     Small
42      41.5689 39      Small
43      59.9547 59      Large
44      46.6482 136     Small
45      55.733  73      Large
46      43.977  180     Small
47      37.4567 20      Large
48      40.3858 49      Large
49      43.2735 107     Small
50      49.7031 100     Large
51      43.4421 180     Large
52      50.0051 83      Large
53      48.7011 247     Large
54      55.1619 102     Small
55      45.6669 83      Small
56      53.5955 105     Large
57      39.6164 114     Small
58      67.3802 62      Large
59      60.3648 93      Small
60      65.0431 37      Large

As part of a disability services research project, an MPH student is analyzing data from a special survey conducted in Missouri. This survey was adapted from the Behavioral Risk Factor Surveillance System (BRFSS). The survey was a random digit dial telephone survey conducted in six Missouri counties between 2010 and 2012. The sample consisted of 3,343 adults: 1,380 from rural and 1,963 from nonrural areas. The survey collected information on residential information and the presence of a disability. Disability was defined as “activities are limited in any way because of an impairment or health problem.” The student hypothesized that disability would be increased in rural areas.

1. What kind of study is this and why?
2. What are the main concerns to make the causal inference based on the data from this study?

The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data5.dat gives the scores of 60 students who did this. How can we relate the two tests?

(a) Plot the data with SAT on the x axis and ACT on the y axis. Describe the overall pattern and any unusual observations.

(b) Find the least-squares regression line and draw it on your plot. Give the results of the significance test for the slope. (Round your regression slope and intercept to three decimal places, your test statistic to two decimal places, and your P-value to four decimal places.)

(c) What is the correlation between the two tests? (Round your answer to three decimal places.)

obs     sat     act
1       950     17
2       719     19
3       648     17
4       905     22
5       1263    29
6       995     25
7       1184    25
8       672     13
9       882     17
10      1082    21
11      875     17
12      951     20
13      1045    22
14      679     19
15      794     18
16      722     16
17      1227    28
18      746     14
19      1145    27
20      716     19
21      1208    28
22      950     21
23      890     23
24      761     17
25      969     17
26      647     11
27      857     21
28      991     21
29      798     17
30      666     14
31      761     19
32      660     20
33      631     16
34      1121    26
35      978     26
36      883     18
37      807     18
38      895     19
39      1184    23
40      869     17
41      582     14
42      1070    20
43      642     16
44      937     23
45      1086    27
46      1013    26
47      713     19
48      1144    25
49      990     24
50      878     16
51      870     26
52      1090    27
53      1095    26
54      781     19
55      1046    21
56      675     13
57      1257    25
58      1099    27
59      620     10
60      714     13

explain how experimental design, analysis of variance, and chi square test are used in research.

A recent study of undergraduates looked at gender differences in dieting trends. There were 182 women and 109 men who participated in the survey. The table below summarizes whether a student tried a low-fat diet or not by gender:

(a) Fill in the missing cells of the table.

(b) Summarize the data numerically. What percent of each gender has tried low-fat diets? (Round your answers to two decimal places.)

(c) Test that there is no association between gender and the likelihood of trying a low-fat diet. (Round your χ² to three decimal places, and round your P-value to four decimal places.)

Summarize the results.

There is strong evidence at the 5% level that gender and the likelihood of trying a low-fat diet are related.There is no evidence at the 5% level that gender and the likelihood of trying a low-fat diet are related.   

An engineer wishes to determine if the stopping distance for midsize automobiles is different from that of compact automobiles at 75 mph. The data is shown below.

Automobile 1 2 3 4 5 6 7 8 9 10

Midsize 188 190 195 192 186 194 188 187 214 203

Compact 200 211 206 297 198 204 218 212 196 193

a) State the null and alternate hypotheses.

b) Use a Wilcoxon rank sum test to determine if there is a difference in the stopping distances between Midsize and compact cars. Copy and paste the results of the test into your Word document.

c) Include a carefully-worded conclusion in the both statistical terms and in the context of the problem. (Label each part)

2. Purchasing a Home in Upstate New York A quantitatively savvy, young couple is interested in

purchasing a home in northern New York. They collected data on 26 houses that had recently sold in

the area. They want to predict the selling price of homes (in thousands of dollars) based on the size

of the home (in square feet).

The regression equation is: Price ̂ = -86.097 + 0.248*Size

Regression Statistics

Multiple R 0.745865819

R Square 0.55631582

Adjusted R Square 0.537828979

Standard Error 162.8663093

Observations 26

              Coefficients StandardError    t Stat              P-value

Intercept -86.097322 82.2443144       -1.0468483      0.30559862

Size      0.24792500 0.04519506       5.48566590     1.22193E-05

a. What is the correlation of the data set? Use the correlation value to help describe the association

shown in the data.

b. Write down the regression equation and then use it to predict the selling price of a home that is

1,742 square feet in size.

c. One home in the data set is 1,400 square feet and costs $187,000, calculate the residual for this

home.

d. What is the slope of the regression line? Interpret the slope in context.

e. If it would make sense, provide a clear interpretation of the intercept of the regression line, in

context. Otherwise, explain why the interpretation does not make sense.

f. What are the degrees of freedom for constructing a confidence interval for, or performing a test

for the effectiveness of the model using slope or correlation?

g. Construct and interpret a 95% confidence interval for the population slope.

h. Use the computer output to do a slope test to determine whether size is an effective linear

predictor of the selling price of recently sold homes. Use a significance level of 5%. Include and

label all six steps of a formal test of hypothesis for regression using slope.

i. We could also use the value of the sample correlation to find a test statistic and p-value to test the

effectiveness of the model. Use the sample correlation, r, to find the test statistic and p-value.

Compare these to the results of part h).

j. What is the R2

for this model? Interpret it in context.

Suppose the scores of a certain high school diploma test follow a normal distribution in the population with a mean of 195 and standard deviation of 30.

1. About ______ percent of the students have a score between 135 and 195.

2. About ______ percent of the students have a score between 225 and 255.

3. The middle 95% of the students have a score between ________  and ________   .

4. Recently class A just had a Math exam, but class B had a Verbal exam.

- Joe in class A has a math score of 160, and all the math scores in class A have a mean of 140 and a standard deviation of 10.

- Eric in class B has a verbal score of 80, and all the verbal scores in class B have a mean of 50 and a standard deviation of 12.

Let’s assume students in classes A and B have very similar academic background, and both classes are hugh classes with lots of students. Then roughly speaking, relative to their respective classmates, who did better in the recent exam, Joe or Eric?

5. A sample consists of 26 scores. What is the degrees of freedom for the sample standard deviation?​

Measures of Disease Frequency (Chapter 2)

In 2009, President Obama launched a nationwide initiative to end homelessness in the U.S. by 2020. The homeless are a vulnerable population with limited access to health care and poor health outcomes. In order to allocate sufficient federal and local resources to eliminate homelessness, U.S. cities conduct an annual survey to estimate the number of homeless persons living within major cities. The City of Boston’s Emergency Shelter Commission (ESC) conducted a survey of homelessness on the night of January 25, 2017. Volunteers counted the number of homeless persons living on the streets, in emergency shelters for individuals or families, in domestic violence programs, in residential mental health or substance abuse programs, transitional housing, and in specialized programs.

1. Which of the following best describes the homeless population in the City of Boston?

a. Dynamic population

b. Fixed population

2. Which of the following describes the homeless population that took part in the ESC survey on January 25^th?

a. Dynamic population

b. Fixed population

3. The 2015 Homeless Census counted 3,456 homeless persons in Boston. The 2016 homeless census counted 3,384 homeless persons in Boston. The size of the population in Boston was 665,984 in 2015 and 673,184 in 2016. From 2015-2016, did the burden of homelessness:

a. Increase

b. Decrease

c. Stay the same (2015: .52%, 2016 0.50%)

d. Cannot determine from this information

4. What do you consider to be the biggest limitation in the homeless survey and why?

a. Time of year (winter)

b. Survey conducted one time annually, not more frequently

c. Survey unlikely captured all homeless persons

d. Survey captures prevalence, not incidence of homelessness

PLEASE SOLVED THIS PROBLEM BY HAND AND IN MINITAB:

The following data are direct solar intensity measurements (watts/m²) on different days at a location in southern Spain: 562, 869, 708, 775, 775, 704, 809, 856, 655, 806, 878, 909, 918, 558, 768, 870, 918, 940, 946, 661, 820, 898, 935, 952, 957, 693, 835, 905, 939, 955, 960, 498, 653, 730, and 753. Calculate the sample mean and sample standard deviation. Prepare a dot diagram of these data. Indicate where the sample mean falls on this diagram. Give a practical interpretation of the sample mean.

Give me a scenario using the probability technique to include the mean, weighted mean, median and mode for populations and samples

A researcher wishes to​ estimate, with 90​% ​confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within 5​% of the population proportion. ​

(a) No preliminary estimate is available. Find the minimum sample size needed. ​

(b) Find the minimum sample size​ needed, using a prior study that found that 40​% of the respondents said they eat fast food four to six times per week. ​

(c) Compare the results from parts​ (a) and​ (b).

Homer is studying the relationship between the average daily temperature and time spent watching television and has collected the data shown in the table. The line of best fit for the data is yˆ=−0.6x+94.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables.

Temperature (Degrees) 40506070 Minutes Watching Television 70655952

(a) According to the line of best fit, what would be the predicted number of minutes spent watching television for an average daily temperature of 39 degrees? Round your answer to two decimal places, as needed.

Provide your answer below:

The predicted number of minutes spent watching television is:

And is the answer:

A: reliable and reasonable

B: unreliable but reasonable

C: unreliable and unreasonable

D: reliable but unreasonable

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s: ??(1)= 1/2 ??(2)= 1/2 ??(3)= 1/3 ??(4)= 2/3

Answer the following questions

(a) Write down the joint PMF

(b) Calculate?(?+?≤5)and?(? −?≥2) 2 ?2+1

(c) Calculate ?(?? ), ?(? ? ), E ? −2
(d) Calculate the C??(?, ? ), C??(1 − ?, 3? + 2) and V??(2? − ? )

(?*) Calculate C??(??, ?), C??(??, ? + ? ) and V?? ?