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Statistics Problems Task

Statistics Problems Task

  • 28th Sep, 2021
  • 17:24 PM

STAT 200 Week 5 Homework Problems

7.1.2

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.

Ans: Here “p” is the proportion of complaints for identity theft from Alaska is the Random variable here.
Here =0.23 is the population parameter.
Hypothesis-> Ho: p=0.23 vs Ha: p<0>

7.1.6 

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.

Ans: Type 1 error: Concluding that the proportion of complaints for identity theft is less than 0.23 but in reality it is not.

Consequence: Here we’ll underestimate the proportion of identity theft.
Type II error: Concluding that the proportion is not less than 0.23 but in reality it is
Consequence: Here we’ll overestimate the proportion of identity theft.

7.2.4

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.
Ans: Here we’ll be using Z-test for proportion. The test statistic is given by:

Where =, the tests statistic follows a standard normal distribution under the null hypothesis. Thus the critical value at level of significance 0.05 is Z=-1.45, but the test statistic is -0.526. Thus we fail to reject the null hypothesis.

7.2.6

In 2008, there were 507 children in Arizona out of 32,601 who were diagnosed with Autism Spectrum Disorder (ASD) ("Autism and developmental"). 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.
Ans: Here we’re testing Ho: vs Ha: . Here we’ll be using Z-test for proportion. The test statistic is given
by:Z=p-p p*(1-p)32601

Where =, p=50732601, the tests statistic follows a standard normal distribution under the null hypothesis. Thus the critical value at level of significance 0.01 is =2.326. The test statistic is 7.134> Z critical. Thus we reject the null hypothesis.

7.3.6
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.

Table #7.3.8: Economic Dynamism of Middle Income Countries
25.8057 37.4511 51.915 43.6952 47.8506 43.7178 58.0767
41.1648 38.0793 37.7251 39.6553 42.0265 48.6159 43.8555
49.1361 61.9281 41.9543 44.9346 46.0521 48.3652 43.6252
50.9866 59.1724 39.6282 33.6074 21.6643

Ans: This part is done in R please have a look on it.

7.3.8

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.
Table #7.3.10: Forward/backward Sway (in mm) of Elderly Subjects
19 30 20 19 29 25 21 24 50

Ans: This part is done in R please have a look on it.
 

8.1.4

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?

Ans: The margin of error is inversely proportion to square root of the sample size. Thus as we decrease the sample size the Margin of error will increase , hence width of the confidence interval increases.

8.1.8
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.

Ans: We’re 96% confident that the true proportion will lie in the above interval.

8.2.6
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 confidence level of 99%.

Ans: This part is done in R please have a look on it.

8.3.6

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.
Table #8.3.9: Economic Dynamism ($) of Middle Income Countries
25.8057 37.4511 51.915 43.6952 47.8506 43.7178 58.0767
41.1648 38.0793 37.7251 39.6553 42.0265 48.6159 43.8555
49.1361 61.9281 41.9543 44.9346 46.0521 48.3652 43.6252
50.9866 59.1724 39.6282 33.6074 21.6643

Ans: This part is done in R please have a look on it.

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