91Ó°ÊÓ

A national survey of$1000$adults was conducted.

Per cent of Americans that believe that big-time college sports programs corrupt the process of higher education = $49\%\text{to}55\%$

Confidence level =$95\%$

The confidence interval = $(0.49,0.55)$

Calculating the error bound = $\frac{\text{Upper limit-lower limit}}{2}=\frac{0.55−0.49}{2}=0.03$

Calculating the point estimate =$\frac{\text{Upper limit+lower limit}}{2}=\frac{0.55+0.49}{2}=0.52$

A national survey of$1000$adults was conducted.

Per cent of Americans that believe that big-time college sports programs corrupt the process of higher education =$49\%-55\%$

Confidence level =$95\%$

As the confidence interval includes values$≤0.50$we can not conclude that more than half of all American adults believe this.

A national survey of $1000$adults was conducted.

Per cent of Americans that believe that big-time college sports programs corrupt the process of higher education =$49\%-55\%$

Confidence level =$95\%$

Given,

n= $100$and confidence interval= $75\%$

$⇒\mathrm{Î\pm }=1−0.75=0.25$

Now, Z= $1.15$and point estimate =$0.52$

Calculating the error bound = $1.150\sqrt{\frac{0.52×0.48}{1000}}=0.018$

Confidence interval = point estimate $Â\pm$error bound$⇒(0.52Â\pm 0.018)$

Hence the confidence interval = $(0.502,0.538)$

A national survey of$1000$ adults was conducted.

Per cent of Americans that believe that big-time college sports programs corrupt the process of higher education =$49\%-55\%$

Confidence level =$95\%$

Yes, as the confidence interval does not lie below $0.50$we can conclude that at least half of all American adults believe this.