$2.$ Lipton Tea Company conducted a mall intercept study at six regional malls around the country and found that $20\%$ of the public preferred tea over coffee as a midafternoon hot drink. This year, Lipton wants to have a nationwide telephone survey performed with random digit dialing. They want to calculate the sample size so that the sample error is $+2\mathrm{.}5$ at $99\%$ confidence interval? What is the value of z at $99\%$ confidence interval

$3$ Lipton Tea Company conducted a mall intercept study at six regional malls around the country and found that $20\%$ of the public preferred tea over coffee as a midafternoon hot drink. This year, Lipton wants to have a nationwide telephone survey performed with random digit dialing. They want to calculate the sample size so that the sample error is $+2\mathrm{.}5$ at $99\%$ confidence interval. What is the value of p and q here.

p$=20\%$

q$=20\%$

q$=80\%$

p$=100\%$

$4.$Lipton Tea Company conducted a mall intercept study at six regional malls around the country and found that $20\%$ of the public preferred tea over coffee as a midafternoon hot drink. This year, Lipton wants to have a nationwide telephone survey performed with random digit dialing. For calculating the sample size, what will be the value of q $?$

$5.$ Lipton Tea Company conducted a mall intercept study at six regional malls around the country and found that $20\%$ of the public preferred tea over coffee as a midafternoon hot drink. This year, Lipton wants to have a nationwide telephone survey performed with random digit dialing. What sample size should be used in this year's study so that the sample error is $+2\mathrm{.}5\%$ at $99\%$ confidence interval? $($Round up to the nearest whole number$)$

$6.$ ACI$$s market research team is going conducting a survey of prospective buyers of a new ceramic material. The research team plans a study using about $100$ companies as a means of determining market demand. After some background research, a total of $312$ companies located in the continental United States are found. What is the population in this example?

$6.$ ACI$$s market research team is going conducting a survey of prospective buyers of a new ceramic material. The research team plans a study using about $100$ companies as a means of determining market demand. After some background research, a total of $312$ companies located in the continental United States are found. What is the sample size in this example?

$7.$ ACI$$s market research team is conducting a survey of prospective buyers of a new ceramic material. The research team plans a study using about $100$ companies as a means of determining market demand. After some background research, a total of $312$ companies located in the continental United States are found. How should this finding impact the final sample size of the survey, given that the population$(312$ companies$)$ is a small population compared to the desired sample size? $($round up to the nearest whole number$)$