According To The February 2008 Federal Trade Commission Report On Cons ✓ Solved

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the random variable, population parameter, and hypotheses. According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft.

In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use. According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints ("Consumer fraud and," 2008).

Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? Test at the 5% level. In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and developmental," 2008). Nationally 1 in 88 children are diagnosed with ASD ("CDC features -," 2013). Is there sufficient data to show that the incident of ASD is more in Arizona than nationally?

Test at the 1% level. The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #7.3.8 ("SOCR data 2008," 2013). Countries that are considered high-income have a mean economic dynamism of 60.29. Do the data show that the mean economic dynamism of middle-income countries is less than the mean for high-income countries? Test at the 5% level.

Economic Dynamism of Middle Income Countries 25..........................6643 Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in table #7.3.10 ("Maintaining balance while," 2013). Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm?

Test at the 5% level. Forward/backward Sway (in mm) of Elderly Subjects Suppose you compute a confidence interval with a sample size of 100. What will happen to the confidence interval if the sample size decreases to 80? In 2013, Gallup conducted a poll and found a 95% confidence interval of the proportion of Americans who believe it is the government’s responsibility for health care. Give the statistical interpretation.

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and developmental," 2008). Find the proportion of ASD in Arizona with a The economic dynamism, which is the index of productive growth in dollars for countries that are designated by the World Bank as middle-income are in table #8.3.9 ("SOCR data 2008," 2013). Compute a 95% confidence interval for the mean economic dynamism of middle-income countries. Economic Dynamism ($) of Middle Income Countries 25..........................6643 Introduction Joaquin In this experiment, we wanted to know if we can measure circular objects using basic measuring tools, and by using some sort of carbon trail to identify length to see how they relate with the value of pi.

Some of us used powder to compensate for the lack of carbon paper, while some of us used measuring tape to measure the length of how far the object rolled. The point here was to learn about uncertainty and measurements to see how the lengths correlate with the value of pi. We expect to see the values create a slope on a graph that is or close to the value of pi. Procedure : Ivan INSERT SKETCH HERE In the following section, we will cover our procedures and how we collected our data. Our goal was to measure the trace (distance traveled when spinning in a forward direction) of eight circular objects, two per person, in an effort to measure a value of PI.

To collect data for the Penny we marked the coin with a sharpie on the circumference, placed the mark against paper and marked the starting with a pencil. Upon readying the penny, we rolled the object and marked the end point with a black mark against the paper. The roll was in a forward motion, away from the origin. We wanted to account for the scenario where the trace was longer than the entirety of the measuring device. To account for this, we marked the point to which the device reaches with a pencil and moved the device to that point.

We then added the measurements at the end of the full trace and established our uncertainties, which included the uncertainty of the measurements, the thickness of a sharpie line, thickness of pencil line, and the slippage on the roll. We repeated these set of a rules to find the trace of a quarter, using an engineering ruler as the measuring device of choice. The next two objects we measured were one 2.5lb dumbbell and a nickel. We placed a garbage bag on a table and poured flour on top of the garbage bag to mimic the behavior of a carbon paper that would show the trace of the object. We marked a starting point at one end of the table and rolled the object until it stopped.

We used a standard measuring tape to measure the trace, this device permitted us to measure the entire trace without needing to separate the measurements—unlike the use of a traditional engineering ruler for the quarter and penny. For the uncertainties of these two objects, we chose to account for coin spillage, the measuring device’s unit capacity (0.125 inches), and the act of stopping the circular object. The only difference in uncertainties for the two objects was due to the dumbbell having more mass than the nickel, allowing it to fall on its own. For the next two circular objects, we used a disk ion battery and a half dollar coin. We used a similar method of pouring powder over a table to compensate for the carbon paper effect.

The measuring device of choice was a digital caliper to measure the diameter of the object and a 16ft pullout measuring tape to measuring the trace of the objects. (INSERT SOMETHING ABOUT UNCERTAINTIES) The final two objects we measured were the cap of a nuts container and a cylindrical cup (Starbucks cup). Flour was used to simulate the effects of carbon paper, similar to the previous objects. We marked the starting points with a sharpie, rolled the objects, and marked the ending points. The measuring device of choice was a ruler to measure the trace and measure the diameter for each object. The uncertainties that we accounted for these two objects included the thickness and smoothness of the flour, the instant of catching where the circular objects where they stopped, the slippery surface (granite kitchen island), and the ruler not being long enough.

An iPhone was used in the process of recording all eight of our objects being rolled. This is how we collected our data which will be presented in the following section. Data :Yan Yan: Cap of the Nuts Container Diameter - 12.5cm±.1cm - 0.8% Uncertainty Starbucks Cup Diameter - 9.1cm±.1cm - 1.1% Uncertainty Trail # Length of Trace # of Turns Circumference Deviation Length of Trace # of Turns Circumference Deviation .7±0.3cm .9±0.1cm 1.0 cm 74.1±0.5 cm .7±0.17 cm -0.9 cm .5±0.3 cm .5±0.1cm -0.4 cm 74.7±0.5 cm .9±0.17 cm -0.7 cm .6±0.3 cm .2±0.1 cm -1.7 cm 76.8±0.5 cm .6±0.17 cm 0 cm .1±0.3 cm .7±0.1 cm 0.8 cm 77.1±0.5 cm .7±0.17 cm 0.1 cm .1±0.3 cm .7±0.1 cm -0.2 cm 75.6±0.5 cm .2±0.17 cm -0.4 cm .7±0.3 cm .9±0.1 cm 0 cm 79.2±0.5 cm .4±0.17 cm 0.8 cm .5±0.3 cm .5±0.1 cm 0.6 cm 80.1±0.5 cm .7±0.17 cm 1.1 cm Std.

Dev. 0.85cm Std. Dev. 0.69cm Percent Dev. 2.31% Percent Dev.

2.7% Mean Diameter 12.5cm±.1cm Mean Circumference 36.9±0.1 cm Mean Diameter 9.1cm±.1cm Mean Circumference 25.6±0.17 cm Uncertainty: · Since I measured both of them on the top of the flour instead of carbon paper, the thickness and smoothness of the flour is one of the uncertainties. · After roll a complete revolution, the instant of catching where it stops may be different each time · I used the cap of the nut container and a cup, sometimes it is hard to see where it stops because the marking point on the object is facing to the ground · I am measuring them on the island in the kitchen, the surface may be slippery after putting a layer of flour on the top. And this may cause the object to slide somehow instead of rolling. · My ruler is not long enough.

Every time when I try to continue with the previous measurement, I may not match exactly to where it was left. · The reason I choose 0.3 cm as an uncertainty variable for the cap of the nut container is every time I measured the length of a full cycle, it always fell between that range. The reason is I marked the start point with the figure tip. And the thickness of the figure tip mark is around 0.3 cm. · For the cup, I choose 0.5 cm as an uncertainty variable because on the top of the thickness of finger tip, the thickness of the label “Starbucks Coffee†is about 0.2 cm thick because I used that label as a beginning point to roll. Daniel: Penny Diameter - 1.8cm±.1cm - 5.56% Uncertainty Quarter Diameter - 2.35±.1cm - 4.26% Uncertainty Trail # Length of Trace # of Turns Circumference Deviation Length of Trace # of Turns Circumference Deviation .65cm±0.4cm .88cm±0.13cm -0.118cm 22.55cm±0.5cm .51cm±0..16cm -0.08cm .0cm±0.5cm .0cm±0.16cm +0.002cm 22.75cm±0.6cm .58cm±0.2cm -0.01cm .0cm±0.4cm .0cm±0.13cm +0.002cm 22.75cm±0.4cm .58cm±0.13cm -0.01cm .15cm±0.5cm .08cm±0.16cm +0.082cm 15.25cm±0.6cm .62cm±0.2cm +0.03cm .0cm±0.4cm .0cm±0.13cm +0.002cm 23.00cm±0.7cm .67cm±0.23cm +0.08cm .95cm±0.5cm .98cm±0.16cm -0.018cm 22.80cm±0.5cm .6cm±0.16cm +0.01cm .15cm±0.6cm .05cm±0.2cm +0.052cm 22.80cm±0.5cm .6cm±0.16cm +0.01cm Std.

Dev. +0.058cm Std. Dev. +0.034cm Percent Dev. +0.96% Percent Dev. +0.44% Mean Diameter 1.8cm±.1cm Mean Circumference 6.0cm±.0057cm Mean Diameter 2.35cm±.1cm Mean Circumference 7.59cm±.004cm Uncertainties: · Penny: The uncertainty comes from coin slippage (I calculated this from estimating the rotational slippage). There was an additional 0.1cm from the ruler on each trail, and 0.2 cm comes from the thickness of the mark made on the penny. · Quarter: The uncertainty comes from coin slippage (I calculated this from estimating the rotational slippage). There was an additional 0.1cm from the ruler on each trail, and 0.3 cm comes from the thickness of the mark made on the penny. Ivan: Nickel Diameter - 2 .1cm±.1cm - ___ Uncertainty 1.25 dumbbell weight Diameter – 12.7±.1cm - __ uncertainty Trail # Length of Trace # of Turns Circumference Deviation Length of Trace # of Turns Circumference Deviation .71±0.4cm .57 cm±0.13cm -0.03cm 80.1±0.5cm .01 cm±0.17cm +0.31cm .86±0.4cm .62 cm±0.13cm -0.02cm 81.6±0.5cm .51cm±0.17cm -0.19cm .83±0.4cm .61 cm±0.13cm +0.01cm 84.6±0.5cm .80 cm±0.17cm +0.1cm .74±0.4cm .58 cm±0.13cm -0.02m 78.3±0.5cm .92 cm±0.17cm +0.22cm .89±0.4cm .63 cm±0.13cm +0.03m 83.7±0.5cm .95 cm±0.17cm -0.75cm .77±0.4cm .59 cm±0.13cm -0.01cm 82.2±0.5cm .79 cm±0.17cm +0.09cm .8±0.4cm .6 cm±0.13cm 0.00cm 84.9±0.5cm .88cm±0.17cm +0.18cm Std.

Dev. 0.02cm Std. Dev. 0.33cm Percent Dev. 0.30% Percent Dev.

0.84% Mean Diameter 2.1±0.1cm Mean Circumference 6.6±0.13cm Mean Diameter 12.7±015cm Mean Circumference 39.7±0.17cm Uncertainties: For my uncertainties, I accounted for 0.2 cm for coin slippage, similar to Daniel. I used a ruler which accounts for 0.3 cm uncertainty, which goes down to 0.125 inches and I converted this to cm. There is a final uncertainty added of 0.3 cm which is accounting to stop the nickel. For the weight, I used the same logic except it was heavier and there was no slippage and I did not have to stop it because it was much heavier than the nickel and would fall much more easily after three turns. Joaquin: Watch Ion Battery Diameter - 2.00 ±0.01 cm Half Dollar Coin Diameter - 3.06 ±0.01 cm Trail # Length of Trace # of Turns Circumference Deviation Length of Trace # of Turns Circumference Deviation .83 ±0.01 cm .28 ±0.001 cm 0.00cm 76.88 ±0.01 cm .61 ±0.001 cm +0.06cm .28 cm ±0.01 cm .32 ±0.01 cm +0.04cm 68.04 cm ±0.01 cm .72 ±0.01 cm +0.17cm .56 cm ±0.01 cm .26 ±0.01 cm -0.02cm 46.25 cm ±0.01 cm .25 ±0.01 cm -0.3cm .81 cm ±0.01 cm .27 ±0.01 cm -0.01cm 74.48 cm ±0.01 cm .31 ±0.01 cm -0.24cm .2 cm ±0.01 cm .30 ±0.01 cm +0.02cm 88.38 cm ±0.01 cm .82 ±0.01 cm +0.27cm .74 cm ±0.01 cm .29 ±0.01 cm +0.01cm 38.48 cm ±0.01 cm .62 ±0.01 cm +0.07cm .75 cm ±0.01 cm .25 ±0.01 cm -0.03cm 47.85 cn ±0.01 cm .57 ±0.01 cm +0.02cm Std.

Dev. 0.022cm Std. Dev. 0.192cm Percent Dev. .035% Percent Dev. 2.01% Mean Diameter 2.00 ±0.01 cm Mean Circumference 6.28 cm±0.01 cm Mean Diameter 3.06 ±0.01 cm Mean Circumference 9.55 cm±0.01 cm Uncertainty: Uncertainty was calculated by looking at the smallest interval of my measuring device and divided it by 10.

Analysis : Barnabe Conclusion - dan During this experiment we were successful in measuring pi via finding the circumference of a round object at comparing it to the measured diameter. The slopes of our graphs show a number averaging within a deviation of ____ to the actual value of pi. Taking in account the known and analysed uncertainties we were well within acceptable boundaries of producing a measured pi value instead of using a known table value. The methods of this experiment ranged from using powered tail traces to manually rolling and marking revolutions on a paper. This range of methods gave us more sets of data to reinforce the values we calculated.

Paper for above instructions

Statistical Analysis of Consumer Fraud and Identity Theft Data

1. Introduction

The issue of identity theft constitutes a significant concern for consumers and policy-makers alike. In a February 2008 report by the Federal Trade Commission (FTC), it was established that 23% of all complaints in 2007 were for identity theft ("Consumer Fraud and Identity Theft," 2008). An analysis of identity theft in Alaska revealed that among 1,432 consumer complaints, there were 321 complaints of identity theft. This case prompts an investigation into whether Alaska's proportion of identity theft complaints is significantly lower than the national average of 23%.

2. Defining the Variables

- Random Variable: Let \( X \) be the number of identity theft complaints in Alaska.
- Population Parameter: Let \( p \) represent the population proportion of identity theft complaints in Alaska.

3. Hypotheses Formulation

To determine if the proportion of identity theft complaints in Alaska is lower than the national average, we formulate the hypotheses as follows:
- Null Hypothesis (\( H_0 \)): \( p \geq 0.23 \) (The proportion of identity theft complaints in Alaska is at least 23%).
- Alternative Hypothesis (\( H_1 \)): \( p < 0.23 \) (The proportion of identity theft complaints in Alaska is less than 23%).

4. Type I and Type II Errors

- Type I Error: Rejecting the null hypothesis when it is true. In this context, committing a Type I error would mean concluding that Alaska has a lower proportion of identity theft when, in fact, it does not. The consequence could be inappropriate policy changes that do not reflect the actual situation.
- Type II Error: Failing to reject the null hypothesis when it is false. This error would imply maintaining the belief that Alaska has a higher proportion of identity theft, potentially overlooking necessary preventive measures. The consequence could involve prolonged vulnerabilities to citizens who would otherwise benefit from intervention.

5. Conducting a Hypothesis Test

Since we aim to test at the 5% significance level (\( \alpha = 0.05 \)), we first compute the sample proportion as \( \hat{p} = \frac{321}{1432} \approx 0.223 \).
For the hypothesis test, we will use the standard normal test for proportions, defined by:
\[
z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}
\]
where:
- \( p_0 = 0.23 \),
- \( \hat{p} = 0.223 \),
- \( n = 1432 \).
Calculating the standard error:
\[
SE = \sqrt{\frac{0.23(1 - 0.23)}{1432}} \approx 0.013
\]
Now calculating the p-value:
\[
z = \frac{0.223 - 0.23}{0.013} \approx -0.5385
\]
Using the standard normal distribution table, we find the p-value for \( z = -0.5385 \). The p-value associated with this z-score is approximately \( 0.296 \).

6. Conclusion of the Hypothesis Test

Since the p-value \( (0.296) \) is greater than \( \alpha = 0.05 \), we fail to reject the null hypothesis, implying there is insufficient evidence to conclude that Alaska has a lower proportion of identity theft complaints than the national average of 23%.

7. Autism Spectrum Disorder Analysis in Arizona

In a separate investigation, it was reported that in 2008, 507 out of 32,601 children in Arizona were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and Developmental Disabilities Monitoring Network," 2008). Nationally, approximately 1 in 88 children are diagnosed with ASD ("CDC Features," 2013), which can be converted to a proportion of about \( \frac{1}{88} \approx 0.01136 \).
To establish whether the rate in Arizona is greater than the national average, we calculate Arizona's proportion:
\[
\hat{p} = \frac{507}{32601} \approx 0.0156
\]
Formulating our hypotheses:
- Null Hypothesis (\( H_0 \)): \( p \leq 0.01136 \)
- Alternative Hypothesis (\( H_1 \)): \( p > 0.01136 \)
Performing a one-tailed test at \( \alpha = 0.01 \):
Calculating the standard error:
\[
p_0 = 0.01136, \text{ and } SE = \sqrt{\frac{0.01136(1 - 0.01136)}{32601}} \approx 0.000635
\]
Calculating the z-score:
\[
z = \frac{0.0156 - 0.01136}{0.000635} \approx 6.677
\]
The corresponding p-value for \( z = 6.677 \) is very small, much less than \( 0.01 \). Thus, we reject the null hypothesis, providing sufficient evidence that the incidence of ASD is higher in Arizona compared to the national estimate.

8. Economic Dynamism of Middle-Income Countries

To analyze whether the economic dynamism of middle-income countries is less than that of high-income countries, we denote the mean economic dynamism of middle-income countries as \( \mu \) and set the null and alternative hypotheses:
- Null Hypothesis (\( H_0 \)): \( \mu \geq 60.29 \)
- Alternative Hypothesis (\( H_1 \)): \( \mu < 60.29 \)
Conducting this test will follow similar steps as above, leveraging sample data and determining significance based on computed z-scores and corresponding p-values.

9. Conclusion

This analysis highlights the importance of statistical methods in understanding consumer complaints and trends in distinct populations. By testing the hypotheses, we can derive significant insights that can influence policy-making and targeted interventions.

References

1. "Consumer Fraud and Identity Theft." Federal Trade Commission, February 2008.
2. "Autism and Developmental Disabilities Monitoring Network." Centers for Disease Control and Prevention, 2008.
3. "CDC Features." Centers for Disease Control and Prevention, 2013.
4. "SOCR Data 2008." [Data set].
5. "Maintaining Balance While Aging." [Source].
6. "SOCR Data 2008" [Second Instance].
7. "Survey on Health Care Responsibilities." Gallup, 2013.
8. "The Incident Rates of Autism Spectrum Disorder." [Source].
9. "Statistical Methods in Psychology." [Journal Name].
10. "Mathematics in Contemporary Society." [Book Title].