STAT 200 Week 5 Homework SOLUTION|GRADED A+

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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.7.1.6 The population proportion=0.23 n=number of complaints=1432 Alaska had complaints=321=x So, sample proportion=nx=1432321 =0.2242 H0: p=0.23 against H1: p<0.23 Z statistic, Z=np^(1−p^)p^−0.23 ~N(0,1) Obs(Z)=(-)0.52 H0: p=0.23 against H1: p<0.23 p value=0.30 (Excel Formula: NORM.S.DIST(0.52,1)) As,p value> α (level of significance). Hence there is not enough evidence to support the claim that, Alaska had a lower proportion of identity theft than 23% . Appropriate level of significance = 0.05 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. H0 : p = 0.23 μ=299,710.5 km/sec μ<299,710.5 lm/sec H1 : p < 0.23 Z critical value = -1.645 at 5% level Sample proportion 'p' = 321/1432 = 0.2242 Z stat = (p - P) / sqrt(PQ/n) This study source was downloaded by 100000831988016 from CourseHero.com on 05-01-2022 11:47:57 GMT -05:00 https://www.coursehero.com/file/38014645/STAT-200-Week-5-Homework-Problemsdocx/ = (0.2242 - 0.23) / sqrt(0.23*1-0.23/1432)= -0.52 Here - Z stat = -0.52 > -1.645 Fail to reject Ho, therefore, there is no sufficient evidence of identity theft lower than 23%. 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. n=32601 x=507 Sample Proportion = 507/32601=0.0156 α=0.01 Ho:p=0.0114 Ha:p>0.0114 This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used. z=(0.0156-0.0114)/sqrt{(0.0114*[1-0.0114])/32601} = 7.061 Since the P-value is p=0, and p=0<0.01, it is concluded that the null hypothesis is rejected. therefore, there is enough evidence to claim that the population proportion p id greater than po, at the α=0.01 significance level. 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 highincome 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 25.805 7 37.451 1 51.915 43.695 2 47.850 6 43.717 8 58.076 7 41.164 8 38.079 3 37.725 1 39.655 3 42.026 5 48.615 9 43.855 5 49.136 1 61.928 1 41.954 3 44.934 6 46.052 1 48.365 2 43.625 2 50.986 6 59.172 4 39.628 2 33.607 4 21.664 3 Sample mean = 43.87 =AVERAGE(C2:I4,G5,F5,E5,D5,C5) This study source was downloaded by 100000831988016 from CourseHero.com on 05-01-2022 11:47:57 GMT -05:00 https://www.coursehero.com/file/38014645/STAT-200-Week-5-Homework-Problemsdocx/ Sample Standard Deviation = 9.7 =STDEV(C2:I4,G5,F5,E5,D5,C5) n=26 Ho: μ=60.29 Ha: μ<60.29 α=0.05 t= (43.87-60.29)/(9.07/sqrt26)=-9.231 Critical value for a left tailed is tc=-1.708 since t=-9.231<tc=-1.708, Ho is rejected. therefore there is enough evidence to claim that the population mean is less than 60.29 at a significance level of 0.05. 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 Sample mean = 26.33 =AVERAGE(C12:K12) Sample standard deviation = 9.77 =STDEV(C12:K12) Ho: μ=18.125 Ha: μ>18.125 α=0.05 Critical value for right tailed tc=1.86 t=(26.33-18.125)/(9.77/sqrt9) = 2.519 Since t=2.519>tc=1.86, it is concluded that the Ho is rejected. Therefore, there is enough evidence to claim that the population mean is greater than 18.125 at a significance level of 0.05. 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? The confidence interval will be larger because the smaller the sample is, the further away from the true population. 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. In 2013, Gallup conducted a poll and found a 95% confidence interval of 0.52<p<0.60, where p is the [Show More]

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