91Ó°ÊÓ

i. per cent of all Asians who would welcome a white person into their families.

$p=0.79$ - sample proportion

$n=251$- sample size

Using normal approximation, we get

role="math" localid="1650867070853" $npandn(1-p)>5$

role="math" localid="1650867993951" $⇒n*(1-p)=52.71>5$

Taking binomial random variable as normally distributed, we get

Standard error is $\sqrt{\left(\frac{p×(1−p)}{n}\right)}$$=0.025709$

Margin error for the confidence interval, $ME=0.0504$

$95\%$confidence interval = Sample mean $Â\pm$ME

role="math" localid="1650867580599" $⇒CI=0.79Â\pm 0.0504$

$⇒CI=(0.7396,0.8404)$

ii. per cent of all Asians who would welcome a Latino into their families.

$p=0.71$- sample proportion

$n=251$- sample size

Using normal approximation, we get

$np\text{and}n(1−p)>5\text{.}$

role="math" localid="1650868008893" $⇒n∗p=178.21>5$

role="math" localid="1650868013813" $⇒n×(1−p)=72.79>5$

Taking binomial random variable as normally distributed, we get

Standard error= $\sqrt{\left(\frac{0.71×(1−0.71)}{251}\right)}$= $0.028641$

Margin error for the confidence interval ME=$0.0561$

$95\%$confidence interval = Sample mean$Â\pm$ME

$⇒CI=0.71Â\pm 0.0561$

$⇒CI=(0.6539,0.7661)$

iii. percent of all Asians who would welcome a black person into their families.

$p=0.66$- sample proportion

$n=251$- sample size

Using normal approximation, we get

$n×(1−p)=85.34>5$

Taking binomial random variable as normally distributed, we get

Standard error = $\sqrt{\left(\frac{0.66×(1−0.66)}{251}\right)}$= $0.0299$

Margin error for the confidence interval ME = $0.0586$

$95\%$confidence interval = Sample mean $Â\pm$ME

role="math" localid="1650868650350" $⇒CI=0.66Â\pm 0.0586$

$⇒CI=(0.6014,0.7186)$

The overlapping confidence intervals are-$(0.7396,0.8404)\text{and}(0.6539,0.7661)$,$(0.6539,0.7661)\text{and}(0.6014,0.7186)$

We can express that there doesn't appear to be a major differentiation between the extent of Asian adults who tell that their families can invite a white individual into their families and furthermore the extent of Asian adults who say that their families can invite a Latino individual into own families.

We can express that there doesn't appear to be a major differentiation between the extent of Asian adults who tell that their families can invite a white individual into their families and furthermore the extent of Asian adults who say that their families can invite a Black individual into own families.