Solution To Week 5 Hw

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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.

Random variable(x) = number of complaints from identity theft in Alaska

Population parameter = proportion of complaints from identity theft in Alaska

Null Hypothesis(H

): p = 0,23

Alternate Hypothesis(H

): p < 0,23

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.

Type I error: Saying p < 0,23 when in fact it isn’t. This would cause the FTC not to treat identity theft in

Alaska as seriously as it should.

Type II error: Saying p = 0,23 when in fact it isn’t. This would cause FTC to spend more resources in

Alaska when it isn’t needed.

Since Type I error would be really damaging to make, we should keep the confidence level high and

alpha level low. In this case an alpha level of 0,01 would be appropriate.

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.

Generally, z-tests are used when we have large sample sizes (n > 30), whereas t-tests are most helpful

with a smaller sample size (n < 30).

We now calculate the critical value of z at 5% (also written as z

0,05

) to be -1,645. The p-value of it is less

than 0,05.

Thus the data doesn’t provide enough evidence for us to reject H

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," 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.





P =





≈ 0,0156

Null Hypothesis(H

): p =





≈ 0,0114

Alternate Hypothesis(H

): p > 0,0114

The P-Value is < 0,01. Thus we can’t reject H

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

Random variable(m) = the mean economic dynamism of middle-income countries

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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. Random variable(x) = number of complaints from identity theft in Alaska Population parameter = proportion of complaints from identity theft in Alaska Null Hypothesis(H0): p = 0,23 Alternate Hypothesis(H1): p < 0,23 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. Type I error: Saying p < 0,23 when in fact it isn’t. This would cause the FTC not to treat identity theft in Alaska as seriously as it should. Type II error: Saying p = 0,23 when in fact it isn’t. This would cause FTC to spend more resources in Alaska when it isn’t needed. Since Type I ...
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