Statistics Essential Questions:

How can you represent relationships between sets and subsets of a sample space?

How do we determine if two events are independent?

How can we interpret the independent or conditional probability of two events?

How can you construct and interpret two-way frequency tables of data?

How can you explain the concepts of conditional probability and independence in everyday situations?

How can you find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model?

How can you apply the Addition Rule and interpret the answer in terms of the model?

How can you use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages?

How can you use statistics to make inferences about a population based on a random sample from that population?

How can you decide whether a specified model is consistent with results from a data-generating process?

How can you use surveys, experiments, and observational studies to make inferences about a population?

How can you define appropriate quantities for descriptive modeling?

How can you use data from a sample survey to estimate a population mean or proportion?

How can we develop a margin of error through the use of simulation models for random sampling?

How can we evaluate reports based on data?

How can we define appropriate quantities for the purpose of descriptive modeling?

1. There are 150 children at summer camp and 71 signed up for swimming. There were a total of 62 children that signed up for canoeing and 28 of them also signed up for swimming. Construct a two-way table summarizing the data.

2. A family has 3 children. What is the probability that all three of them are boys?

3. A group of people were surveyed about whether they have unlimited data on their phone plan and whether they went on a vacation in the past year.

	Vacation	No vacation	Total
Have unlimited data	97	38	135
Do not have unlimited data	14	17	31
Total	111	55	166

What is the probability that a randomly chosen person did not go on vacation in the last year, but carries unlimited data on their plan? Are these two events independent?

4.Using the data from #3, what is the probability of going on a vacation given thatthey do not carry unlimited data on their phone plan?

5. The two-way table below shows data for 446,501 people who responded to the following questions:

Do you have activity limitations as a result of health problems?

Have you ever been diagnosed with a heart attack?

Activity limitations No activity limitations Total

Heart attack 14,823 104,996 119,819 14,044

No heart attack 312,638 326,682

Total28,867 417,634 446,501

Source: Center for Disease Control and Prevention

- What is the probability that a randomly chosen person has had a heart attack and has no activity limitations?

6. There are 12,500 students in the national spelling bee. You scored in the 72nd percentile. How many students scored better than you?

7. The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution. What percentage of children have a mean cholesterol level between 105 mg/dl and 245 mg/dl?

8. GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34. What proportion of freshman biology majors have GPA above 3.55?

9. A doctor wants to know what percentage of her patients get enough sleep regularly. She surveyed 50 of her patients when they came to their regular appointments. She found that 31 reported getting enough sleep each night. Identify the parameter. What statistic should she use to approximate that parameter?

10. Describe a confidence interval. What is the margin of error and how is it used to find the confidence interval?