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.

A) If four babies are born in a given hospital on the same day, what is the probability that all four will be boys?
B) if four babies are born in a given hospital on the same day, what is the probability that 3 will be girls and 1 will be a boy?
C) You flip a coin twice what is the probability that it lands on heads once and tails one?

Please show your calculations and steps. In a recent national survey, 30 Canadian adults aged 18-24 reported having used cannabis for the first time since its legalisation in 2018 compared to 68 among the 25-44-year-olds. Out of the 1500 survey respondents, 125 were 18-24-year-olds and 400 were in the 25-44 age group. The Public Health Agency has been concerned that the first time use of cannabis among the younger cohort is higher than that among the older cohort.

a) Formulate the appropriate statistical hypotheses to test if the proportion of first-time cannabis users is higher among younger adults.

b) Perform the appropriate hypothesis test manually using the P-value approach and a 2% significance level. Make sure you verify that the relevant assumptions and conditions are met for the test.

c) Using the corresponding confidence level, calculate a one-sided confidence interval for the difference in the proportions of first-time cannabis users among the two age groups.

d) Are the results from b) and c) above consistent and why? e) Use Minitab or other appropriate software to perform the calculations in b) and c) and comment on any differences.

Identify at least three different qualitative data collection instruments (e.g. in-depth interviews, focus groups, etc.) and how they can be used in a study.

1. When a pair of balanced dice is rolled. Let A = {the sum of the dice is 10}, B = {doubles are rolled}. Find P(A), P(B).

2. Four couples are randomly sat in a row. How many different ways possible if

(a) no restriction; (b) all men have to sit together and all women have to sit together; (c) one of the couples have to sit together.

3.Two events A and B are investigated. P(A) = 0.35, P(B) = 0.72, the percent of chance that at least one of the event A or B occur is 90%. What is the probability that only one of the events happens

Data Structures for R studio

1. Create a numeric vector containing 10 random numbers ranging from 1 to 10000.
   • Validate that the object you created is a vector
   • Give an example of where you might find this in a biologicall data set.
2. Create a 10-member list containg both numeric and character data.
   • Validate that the object you created is a list
   • Give an example of where you might find this in a biologicall data set.
3. Create a data frame that relates the following variables and corresponding data types:
   • sample (integer): 1,2,3,4,5
   • genus (chharacter): Lupinus,Lupinus, Lupinus,Lupinus, Lupinus
   • species (character): texensis,texensis,texensis,texensis,texensis
   • date_of_flowering (date): Feb 3, 2019,Feb 23, 2019, March 1, 2019,Feb 21, 2019,Feb 22, 2019

1. A researcher wanted to estimate the mean contributions made to charitable causes by all major companies. A random sample of 18 companies produced by the following data on contributions (in millions of dollars) made by them.
1.8, 0.6, 1.2, 0.3, 2.6, 1.9, 3.4, 2.6, 0.2
2.4, 1.4, 2.5, 3.1, 0.9, 1.2, 2.0, 0.8, 1.1

Assume that the contributions made to charitable causes by all major companies have a normal distribution.
a. What is the point estimate for the population mean?
b. Construct a 98% confidence interval for the population mean.
c. What sample size would the researcher need to obtain a margin of error of 100,000 for the same confidence level? (Assume that the sample standard deviation obtained from his original sample is equal to the population standard deviation.)
d. Prior to collecting the data, the researcher believed that the mean contribution of all companies was less than $2.5 million. For a significance level of 0.01, test the researchers hypothesis.

A trucking company would like to compare two different routes for efficiency. Truckers are randomly assigned to two different routes. Twenty truckers following Route A report an average of 49 ​minutes, with a standard deviation of 5 minutes. Twenty truckers following Route B report an average of 54 ​minutes, with a standard deviation of 3 minutes. Histograms of travel times for the routes are roughly symmetric and show no outliers.
​a) Find a​ 95% confidence interval for the difference in the commuting time for the two routes.
​b) Does the result in part​ (a) provide sufficient evidence to conclude that the company will save time by always driving one of the​ routes? Explain.
​a) The​ 95% confidence interval for the difference in the commuting time for the two routes muBminusmuA is ​(
nothing ​minutes,
nothing ​minutes).

Listed below are annual data for various years. The data are weights​ (metric tons) of imported lemons and car crash fatality rates per​ 100,000 population. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using α = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality​ rates? Do the results suggest that imported lemons cause car​ fatalities?

What are the null and alternative​ hypotheses?

A.

H0​: ρ=0

H1​: ρ ≠0

B.

H0​: ρ ≠0

H1​: ρ =0

C.

H0​: ρ=0

H1​: ρ <0

D.

H0​: ρ=0

H1​: ρ >0

Construct a scatterplot. Choose the correct graph below.

The linear correlation coefficient r is _____ .

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

The test statistic t is ____.

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

The​ P-value is _______.

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

Because the​ P-value is ______ (greater / less) than the significance level 0.05​, there _______(is not / is) sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of α= 0.05.

Do the results suggest that imported lemons cause car​ fatalities?

A.

The results do not suggest any​ cause-effect relationship between the two variables.

B.

The results suggest that an increase in imported lemons causes in an increase in car fatality rates.

C.

The results suggest that imported lemons cause car fatalities.

D.

The results suggest that an increase in imported lemons causes car fatality rates to remain the same.

In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .75, the same as the overall proportion of complaints settled in 2008.

Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? (Round to four decimal places) Answer

Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? (Round to four decimal places)

For this, problem, please include the excel procedure you used to arrive at an answer (screenshots, explanation, actual file, etc.).

The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with electronic trades handled by discount brokers. As part of the survey, members were asked to rate their satisfaction with the trade price and the speed of execution, as well as provide an overall satisfaction rating. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker, summary scores were computed by computing a weighted average of the scores provided by each respondent. A portion the survey results follow (AAII web site, February 7, 2012).

A. Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker. Interpret the coefficient of determination.

B. Use the t test to determine the significance of each independent variable. What are your conclusions at the 0.05 level of significance?

C. Interpret the estimated regression parameters. Are the relationships indicated by these estimates what you would expect?

D. Finger Lakes Investments has developed a new electronic trading system and would like to predict overall customer satisfaction assuming they can provide satisfactory service levels (3) for both trade price and speed of execution. Use the estimated regression equation developed in part (a) to predict overall satisfaction level for Finger Lakes Investments if they can achieve these performance levels.

E. What concerns (if any) do you have with regard to the possible responses the respondents could select on the survey

Clinical trials involved treating flu patients with Tamiflu, which is a medicine intended to attack the influenza virus and stop it from causing flu symptoms. Among 724 patients treated with Tamiflu, 72 experienced nausea as an adverse reaction. (a) Construct a 95% confidence interval for the (population) proportion of patients treated with Tamiflu that experienced nausea as an adverse reaction.  

(b) It is reported that the rate of nausea among patients treated with Tamiflu is greater than 7%. Using the current data, test the claim that the rate of nausea among patients treated with Tamiflu is greater than 7%. Use all steps for hypothesis testing to make a conclusion at a significance level of 5%.

(c) What assumptions or conditions have you made in statistical inference in parts (a) and (b) respectively? Are they being satisfied?

Compute in excel

Text Question 8.3.8 (Confidence Interval for a Mean, not a proportion) (adapted) The Table below contains the percentage of women receiving prenatal care in 2009 for a sample of countries. (i) Find the 90% confidence interval for the average percentage of woman receiving prenatal care in 2009 using the normal distribution. (Express as percentages with two digits, as shown in the data.) (ii) Find the 90% confidence interval for the average percentage of woman receiving prenatal care in 2009 using the t-distribution. (Express as percentages with two digits, as shown in the data.) (iii) Are you answers similar? Why or why not? Note: You’ll find the data below reproduced in the Excel answer template. 70.08 72.73 74.52 75.79 76.28 76.28 76.65 80.34 80.60 81.90 86.30 87.70 87.76 88.40 90.70 91.50 91.80 92.10 92.20 92.41 92.47 93.00 93.20 93.40 93.63 93.68 93.80 94.30 94.51 95.00 95.80 95.80 96.23 96.24 97.30 97.90 97.95 98.20 99.00 99.00 99.10 99.10 100.0 100.0 100.00 100.00 100.00 (b) Text Question 8.2.5 (Confidence Interval for a Proportion) In 2013, the Gallup poll asked 1039 U.S. adults if they agreed that a conspiracy was behind the assassination of President Kennedy. And found that 634 did so. Using a 98% confidence interval, estimate the proportion of Americans who believe in this conspiracy. Express both lower and upper bounds as a percentage, rounding to 2 digits, e.g., 57.29, 65.34.