What is the ideal study design from a statistical point of view? -Clinical trial -Observational studies -A&B -None of the above

The centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and Questions Navigation Menu preliminary estimate of the proportion who smoke of .26.
a) How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02?(to the nearest whole number) Use 95% confidence.
b) Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?
c) What is the 95% confidence interval for the proportion of smokers in the population?(to 4 decimals)?

About 4% of the population has a particular genetic mutation. 1000 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 1000. (Remember that means should be rounded to one more decimal place than the raw data.)

HBL Bank Pvt LtD. is studying its ATM use in the Gulshan-e-Iqbal area of Karachi. A sample of 30 ATMs showed they were used in the given number of times (in seconds) on a particular day, as shown in Table 1.
Identify the presence of outliers in this dataset After removing the outliers (if present) from the given dataset, what is the expected or average number of times (in seconds) the ATM is used in the new dataset (if outliers were detected and removed). Show your results with errors in the statistical expected or average value.
$$\overline{)\begin{array}{cccccccccc}83.24& 64.01& 84.23& 76.20& 84.21& 54.29& 5.11& 59.21& 70.23& 61.01\\ 63.10& 80.23& 84.21& 73.20& 68.11& 52.19& 65.22& 90.16& 52.16& 177.21\\ 95.23& 36.15& 48.12& 16.18& 59.32& 84.22& 195.13& 47.18& 87.13& 26.11\end{array}}$$

Using the coefficient of variation, how much (%) do these data sets vary?
(rounding to the nearest percent)
Data Set 1: ${\displaystyle \bar{x}=12\text{and}s=7}$
Data Set 2: ${\displaystyle \bar{x}=0.12\text{and}s=0.3}$

Sketch a scatterplot where the association is nonlinear, but the correlation is close to $[r=-1]$.

A table of values for f,g, f', and g' is given.
$$\begin{array}{|ccccc|}\hline x& f(x)& g(x)& f^{\prime }(x)& g^{\prime }(x)\\ 1& 3& 2& 4& 6\\ 2& 1& 8& 5& 7\\ 3& 7& 2& 7& 9\\ \hline\end{array}$$
a) If h(x)=f(g(x)), find h'(3)
b) If H(x)=g(f(x)),find H'(1).

The following data represent the planned rated capacities in megawatts (millions of watts) for the world’s 20 largest hydroelectric plants.
See Attachment
a. Construct a stem and leaf display for the data.
b. How would you describe the shape of this distribution?
$$\begin{array}{|ccc|}\hline 18,200& 4,500& 3,000\\ 12,600& 4,200& 2,940\\ 10,000& 4,200& 2,715\\ 8,370& 3,840& 2,700\\ 6,400& 3,444& 2,541\\ 6,300& 3,300& 2,512\\ 6,000& 3,100\\ \hline\end{array}$$