Improve Your Understanding of College Level Statistics Problems

Express the confidence interval ${\displaystyle 53.5\mathrm{\%}<p<69.7\mathrm{\%}}$ in the form of $\hat{p}\pm ME$

If ${\displaystyle n=600}$ and ${\displaystyle \hat{p}=0.95}$, construct a ${\displaystyle 95\mathrm{\%}}$ confidence interval.
Give your answer to three decimals.
$<p<$

A survey of several 10 to 11 year olds recorded the following amounts spent on a trip to the mall:
$19.17,$21.18,$20.38,$25.08
Construct the ${\displaystyle 90\mathrm{\%}}$ confidence interval for the average amount spent by 10 to 11 year olds on a trip to the mall. Assume the population is approximately normal.
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Step 4 of 4 : Construct the ${\displaystyle 90\mathrm{\%}}$ confidence interval. Round your answer to two decimal places.

The following data, recorded in days, represents the recovery time, for patients who are randomly treated with one of two medications to cure servere bladder infections:
$\begin{array}{|cc|}\hline Medication1& Medication2\\ n_1=13& n_2=16\\ {\overline{x}}_1=20& {\overline{x}}_2=15\\ s_1^2=2.0& s_2^2=1.8\\ \hline\end{array}$
Find the ${\displaystyle 99\mathrm{\%}}$ confidence interval for ${\displaystyle \mu 1-\mu 2}$, the difference in mean drug recovery times, and INTERPRET it to get a helpful conclusion about the drugs.
Assume normal populations, with equal variances.

Express the confidence interval ${\displaystyle 172.3<\mu <229.1}$ in the form of ${\displaystyle \bar{x}\pm ME.}$

A study a local high school tried to determine the mean height of females in the US. A study surveyed a random sample of 125 females and found a mean height of 64.5 inches with a standard deviation of 5 inches. Determine a ${\displaystyle 95\mathrm{\%}}$ confidence interval for the mean.
$\begin{array}{|cc|}\hline \text{Confidence Interval}& z\\ 80\mathrm{\%}& 1.282\\ 85\mathrm{\%}& 1.440\\ 90\mathrm{\%}& 1.645\\ 95\mathrm{\%}& 1.960\\ 99\mathrm{\%}& 2.576\\ 99.5\mathrm{\%}& 2.807\\ 99.9\mathrm{\%}& 3.291\\ \hline\end{array}$