Statistics and Data Analysis

USE YOUR FIRST NAME AND LAST INITIAL ONLY.

Please write a thoughtful response to the following prompt.  The response should be in complete sentences and reflect the use of proper grammar, spelling, etc.

In the beginning of Chapter 14, the textbook discusses The Law of Large Numbers and how many people misinterpret it.  Create your own, original example illustrating the Law of Large Numbers and discuss a possible misconception (incorrect interpretation/conclusion) that someone may have regarding it.

If you wish to view the rubric that will be used to assess this entry, please visit Ms. Schrier’s website and look in the AP Stat Resources Tab.

Posts must be submitted by 10/24/2010 at 11:59pm.  Posts will not be accepted late.

Last Blog Post of the Year!!  – Due No Later than 10:00pm on Sunday, June 6.

Please answer each probability question based on the given information and explain your process and reasoning in a few sentences each.

Given:  P(A) = 0.26, P(B) = 0.41, P(A ∩ B) = 0.1

a) Find P(A U B). 

b) Find P(B|A).

c) Are A and B disjoint? 

d) Are A and B independent?

Blog Post #17 – Due Sunday, May 30 at 10:00pm

In response to nutrition concerns raised last year about food served in school cafeterias, the Smallville School District entered into a one-year contract with the Healthy Alternative Meals (HAM) Company.  Under this contract, the company plans and prepares meals for 2500 elementary, middle, and high school students, with a focus on good nutrition.  The school administration would like to survey the students in the district to estimate the proportion of students who are satisfied with the food under this contract.

Two sampling plans for selecting the students to be surveyed are under consideration by the administration.  One plan is to take a simple random sample of students in the district and then survey those students.  The other plan is to take a stratified random sample of students in the district and then survey those students.

a) Describe a simple random sampling procedure that the administrators could use to select 200 students from the 2500 students in the district.

b)  If a stratified random sampling procedure is used, give one example of an effective variable on which to stratify in this survey.  Explain your reasoning.

c)  Describe one statistical advantage of using a stratified random sample over a simple random sample in the context of this study.

(This is a question taken from the 2010 Form B AP Exam).

Blog Post #16 – Due no later than 10:00pm on Sunday, May 23.

Directions – Answer each question in a complete paragraph.

Remember:  Compare means discuss similarities; contrast means discuss differences.

1) Compare and contrast Cluster Sampling and Stratified Sampling.  (Examples may be helpful to enhance your explanation).

2) Compare and contrast the use of Hypothesis Tests and Confidence Intervals.  (Focus on when it would be appropriate to use each method of inference and the information you can gain from each method).

Blog Post #15 Due no later than 10:00pm on Sunday, May 16.

For the scenario listed below, answer each question.  If applicable, state the proper probability notation.  Explain in complete sentences how you solved any problems that are marked with a  star*.

The Verbal SAT scores of a certain state are normally distributed with a mean of 460 and a standard deviation of 90.

*a.  State the interval that contains the center 90% of the data.

b.  Elena scored a 410 on the verbal section of the SAT.  Standardize her score.  What proportion of students scored lower than Elena?

c.  What score marked the 85^th percentile?

*d.  This state sponsors a scholarship that seniors may apply for if they score higher than a 750 on the verbal section of the SAT.  If there are 125,000 seniors in the state, about how many of them would be eligible to apply for the scholarship?

e.  If a student is selected at random, what is the probability that he/she scored a 450?

*f.  If a student is selected at random, what is the probability that he/she scores more than a 600?

*g.  If a random sample of 20 students is selected, what is the probability that the mean score is more than 500?

Blog Post #14 – Due at 10:00pm on Sunday, May 9

Scenario:  A manufacturer claims that the mean life of a certain tire is 22,000 miles.  If an inference test shows that the life is less than 22,000 miles, the company will re-evaluate and improve their production process. 

An SRS of 100 tires made by the manufacturer lasted an average of 21,819 miles with a standard deviation of 1,295 miles.

1. Test the null hypothesis m = 22,000 miles against the alternative hypothesis m < 22,000 miles at the 0.05 level of significance.  (State conditions, test statistic, p-value, and conclusion).
2. If the Power for this test against a certain alternative hypothesis is found to be 0.92, what is the probability of a Type I Error?  What is the probability of a Type II Error?
3. Describe in context the consequence of a Type I Error for this situation.
4. Describe in context the consequence of a Type II Error for this situation.
5. Based on your conclusion in question 1, what type of error could have been made for this scenario?

Study for the AP Test. 

Blog Post #12 – Due no later than 10:00pm on Sunday, April 25.

Scenario:  The side effects of a medication are under investigation.  A group of 80 patients with a certain condition are randomly assigned to two treatment groups.  One group of 40 patients will take the new experimental drug (Drug A).  The other group of 40 patients will take the traditional drug (Drug B).  Patients were evaluated and it was determined whether they suffered from any serious side effects (all patients were evaluated in the same manner and a standard method for determining whether serious side effects were present was used.  Patients and evaluators did not know which treatment patients received).  The results of the study are shown in the table below.

Do these results indicate that the proportion of patients who suffered serious side effects taking the experimental drug (Drug A) is less than the proportion of patients who suffered serious side effects taking the traditional medication (Drug B) at a significance level of 0.05?

 In your response, please make sure you include the following:  Name of the inference procedure, assumptions, hypotheses, test statistic, p-value, and conclusion in context.  (Note:  You do NOT need to “show work” instead you must include a clear and thorough written explanation of your procedures).

Blog Post #11 – Due Sunday, 4/18, at 10:00pm

Use the following data table shown below to complete each problem.  (All values of fictitious).

1) Crease a scatter plot of the data (on a piece of paper or using a graphing calculator).  Describe the plot.

2) State the LSR line for the data.

3) State and interpret r.

4) State and interpret r^2.

5) Predict the mean cost of a new Honda Civic in the year 2008.

6) Is the prediction in #5 an example of interpolation or extrapolation?

7) What are the dangers of extrapolation?

Due at 10:00pm on Sunday, April 11

Answer each question regarding inference procedures in complete sentences.

1) One of the conditions for inference is to have a normal population or a sample size greater than or equal to 30.  Explain why this condition is required.

2) A company reports that its mean salary for employees is $60,500.  The union leader of the workers believes that this report is too high.  The union leader takes a random sample of 50 employees and finds a sample mean of $57,850.  The inference test is completed and a p-value of 0.003 is obtained.  Explain what the p-value means.

3) Explain the connection between a two-sided hypothesis test and a confidence interval (In other words, if you fail to reject a null hypothesis at α = 0.05, what will be true about a 95% confidence interval?  If you reject a null hypothesis at α = 0.05, what will be true about a 95% confidence interval?) (It may be helpful to create an example for your explanation).