MATH 2013: Demonstration #1

Please show work and write answers in complete sentences.

I.            In a recent academic year, the average Oklahoma ACT score was 20.5, and the average national ACT score was 21.1. The chart below shows the average ACT scores.

This graph does show that Oklahoma’s average ACT score is lower than the national average. However, what is misleading about the information shown (or not shown) in the graph?

II.          A court-appointed auditor is studying years of experience and salary for nurses at a hospital. The hospital has six floors on which the nurses work. Explain the differences between creating a cluster sample and a stratified sample for this study. You do not have the years of experience or salary data yet – please do not use those variables in the design.

III.        The table below summarizes recent data about hospitalization for heart attack.

Fill in the table below with the requested percentages. Round answers to the nearest hundredth of a percent.

IV.       Tight Hamstring Syndrome (THS) in children has been attributed to a number of disorders. A Meta-Analysis of clinical research in Germany (102 children) between 1980 and 2001 estimated that about 70% of suffered from severe underlying diseases.

[A]   Is this a study involving a binomial variable? If so, what is a “success” in this sample? If not, why not?

[B]   What are the mean (expected value) and standard deviation of this variable? Round to tenths if needed.

[C]   PROBABILITIES: Show the commands that you used on your TI-83/84. Round answers to three decimal places.

1)       What is the probability that exactly 71 of the cases were related to severe underlying diseases?

2)       What is the probability that less than 63 of the cases were related to severe underlying diseases?

3)       What is the probability that no less than 76 of the cases were related to severe underlying diseases?

4)       Would it be unusual if more than 80 cases were related to severe underlying diseases? Support your answer with a calculation and an explanation.

V.         A survey of 1200 randomly selected parents across the Eastern Time zone of the United States asked about tackle football before high school for their kids.

[A]   Fill in the Undecided number. Fill in the second row with relative frequencies as percentages.

[B]   A similar survey in Texas had the percentages shown in the table below. Fill in the Undecided percentage.

[C]   There is a 1.36 percentage point margin of error in the Undecided category of the Texas survey, and there is a 1.76 percentage point margin of error in the Undecided category of the Eastern Time zone survey. Do you think there is a significant difference in the percentage of Undecided parents in these polls? Why or why not? (PLEASE DO NOT GO LOOKING UP FANCY FORMULAS, CALCULATOR PROCEDURES OR TABLES. Keep your answer simple.)