An article regarding interracial dating and marriage recently appeared in a newspaper. Of the 1713 randomly selected adults, 301 identified themselves as Latinos, 325 identified themselves as blacks, 255 identified themselves as Asians, and 778 identified themselves as whites. Among Asians, 79% would welcome a white person into their families, 71% would welcome a Latino, and 66% would welcome a black person.If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)Construct the 95% confidence intervals for the three Asian responses. (Round your answers to four decimal places.)Construct the 95% confidence intervals for the three Asian responses. (Round your answers to four decimal places.)a) Welcome a white peron.b) welcome a black person.c) welcome a latino

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An article regarding interracial dating and marriage recently appeared in a newspaper. Of the 1713 randomly selected adults, 301 identified themselves as Latinos, 325 identified themselves as blacks, 255 identified themselves as Asians, and 778 identified themselves as whites. Among Asians, 79% would welcome a white person into their families, 71% would welcome a Latino, and 66% would welcome a black person.If you are using a Student&#039;s t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)Construct the 95% confidence intervals for the three Asian responses. (Round your answers to four decimal places.)Construct the 95% confidence intervals for the three Asian responses. (Round your answers to four decimal places.)a) Welcome a white peron.b) welcome a black person.c) welcome a latino

MoxboasteBots5h · Accepted Answer

Step 1  From the Standard Normal table, the z value for 95% confidence level is 1.96.  The 95% confidence intervals for the Asian responses &quot;Welcome a white peron&quot; is,  CI=p^±zp^(1−p^)n  =0.79±1.960.79(1−0.79)255  =0.79±0.0499  =(0.7401, 0.8399)  Step 2  The 95% confidence intervals for the Asian responses &quot;welcome a black person&quot; is,  CI=p^±zp^(1−p^)n  =0.66±1.960.66(1−0.66)255  =0.66±0.0581  =(0.6019, 0.7181)  The 95% confidence intervals for the Asian responses &quot;welcome a latino&quot; is,  CI=p^±zp^(1−p^)n  =0.71±1.960.71(1−0.71)255  =0.71±0.0557  =(0.6543, 0.7657)

limacarp4 · Accepted Answer

a) Welcome a white person  p^=0.79  S.E=p^(1−p^)n=(0.79)(0.21)251=0.02571  95%CI=(p^−tα2×S.E, p^+tα2×S.E)  tα2 for df=n−1=250  t0.025, 250=1.9695  ∴95%CI=(0.79−(1.9695)(0.02571), 0.79+(1.9695)(0.0257))  =(0.7394, 0.8406)  b) Welcom a latino  p^=0.71  S.E=p^(1−p^)n=(0.71)(0.29)251=0.02864  95%CI=(0.71−(1.9695)(0.02864), 0.71+(1.9695)(0.02864))  =(0.6536, 0.7664)  c) Welcome a black  p^=0.66  S.E=(0.66)(0.34)251=0.0299  95%CI=(0.66−(1.9695)(0.03), 0.66+(1.96)(0.031))  =(0.6011, 0.7189)

nick1337 · Accepted Answer

Step 1 White Sample size, n=251 We use normal approximation, for this we check that both np and n(1−p)&amp;gt;5 Since n×p=198.29&amp;gt;5 and n×(1−p)=52.71&amp;gt;5, we can take binomial random variable as normally distributed, with mean =p=0.79 and std error =p×(1−p)n=0.025709 For constructing Confidence interval, Margin of Error 95% confidence interval is given by: Sample Mean±(Margin of Error) 0.79±0.0504=(0.7369, 0.8404) Step 2 Latino Sample size n=251 Sample proportion, p=0.71 We use normal approximation, for this we check that both np and n(1−p)&amp;gt;5 Since n×p=178.21&amp;gt;5 and n×(1−p)=72.79&amp;gt;5, we can take binomial random variable as normally distributed, with mean =p=0.71 and std error =p×(1−p)n=0.02864 For constructing Confidence interval, Margin of Error (ME)=z×SD=0.0561 95% confidence interval is given by: Sample Mean±(Margin of Error) 0.71±0.0561=(0.6359, 0.7661) Step 3 Black Sample size n=251 Sample proportion, p=0.66 We use normal approximation, for this we check that both np and n(1−p)&amp;gt;5 Since  and ​n×(1−p)=85.34&amp;gt;5, we can take binomial random variable as normally distributed, with mean =p=0.66 and std error =p×(1−p)n=0.0299 For constructing Confidence interval, Margin of Error  (ME)=z×SD=0.0586 95% confidence interval is given by: Sample Mean±(Margin of Error) 0.66±0.0586=(0.6014, 0.7186)

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