Solutions

Please note that the steps show rounded numbers, but that the final answers to the problems are calculated without rounding.

Problem Part Solution
1 - b. Pie Charts
d. Bar Charts
2 - \(\hat{p} = \frac{x}{n}\)
n = total sample size
x = number of individuals in sample with the characteristic you are focusing on.
3 - P or the population proportion
4 - \(\text{Standard Deviation of } \hat{p} = \sqrt{\frac{p(1-p)}{n}}\)
n = total sample size
p = the true population proportion, which is also the mean of the distribution of \(\hat{p}\)
5 - Answers may vary: Categorical data groups the individuals in your study into categories, while numerical data assigns numbers to the individuals in your study. These numbers are a subset of the real numbers and can be discrete or continuous.
6 - Pie
7 - Bar
8 - Your answers could vary. You could’ve used proportions to describe the data, described the data in words, or displayed a frequency table.
Freshman: Count=8, \(\hat{p}\)=0.0437
Sophmore: Count=75, \(\hat{p}\)=0.4098
Junior: Count=59, \(\hat{p}\)=0.3224
Senior: Count=39, \(\hat{p}\)=0.2131
Other: Count=2, \(\hat{p}\)=0.0109
9 A The mean is 7% or 0.07 in this sample and the standard deviation is 0.0093
9 B z= 1.073
9 C Area = 0.1416