$1.$ A researcher expects the population proportion of Cubs fans in Chicago to be $80$ percent. The researcher wishes to have an error of less than $5$ percent and to be $95$ percent confident of an estimate to be made from a mail survey.

Z $=1\mathrm{.}96$

E $=0\mathrm{.}05$

p $=0\mathrm{.}8$

q $=0\mathrm{.}20$

Calculations:

n$=(1\mathrm{.}92^2$ x$0\mathrm{.}8$x$0\mathrm{.}2)/0\mathrm{.}5^2$

n$=(3\mathrm{.}8416$x$0\mathrm{.}16)/0\mathrm{.}0025$

n$=0\mathrm{.}61456/0\mathrm{.}0025$

n $=245\mathrm{.}86$

n$=246$

The required sample size is $246$

the measures of central tendency and calculate each for the following salary data: $$25,000,$ $$35,000,$ $$35,000,$ $$40,000,$ $$50,000,$ $$70,000,$ and $$350,000.$

Mean $=(25,000+35,000+35,000+40,000+50,000+70,000+350,000)/7$

Mean $=605,000/7$

Mean $$ $$86,428\mathrm{.}5714$

Median$=(7+1)/2=4$

Median$=40,000$

Mode$=35,000($s it is repeated twice$)$

$3.$ Discuss the two basic rules for code construction and give examples of each.

$4.$ Compare and contrast Type I errors and Type II errors and explain which one is of more concern to researchers.