QMB 3200 Sec 521 Homework 9
1qmb 3200 Sec 521homework 9
Solve all the problems. All problems carry 20 points each. Maximum score for Homework #9 is 80 points.
Conduct a sign test to determine if stock splits are beneficial to stockholders based on a sample of 20 stock splits where 15 led to an increase in value, 3 to a decrease, and 2 no change. State hypotheses and determine conclusion at α = .01.
Analyze a poll from 2008 with 600 adults, where responses about their children’s future included 240 expecting a better life, 310 worse, and 50 the same. Use a sign test at α = .01 to assess if there is a difference between the number expecting a better versus a worse life.
Compare delivery times for two overnight mail services with data provided. Use a .10 significance level to determine if median delivery times differ between services.
Evaluate hurricane wind speeds in two regions using data provided, testing at α = .10 whether the distribution of wind speeds differs across regions.
Questions involve calculating the probability related to the sample standard deviation for normally distributed data, determining required sample sizes for estimating population proportions and means, constructing confidence intervals, and testing hypotheses about population parameters based on sample data, including wind speeds, stock splits, and public opinion surveys.
Sample Paper For Above instruction
Introduction
Understanding the benefits of stock splits and assessing public opinions and weather phenomena require rigorous statistical analysis. Sign tests, hypothesis testing, confidence intervals, and probability calculations serve as critical tools in making informed conclusions based on sample data. This paper examines the application of these statistical methods across various scenarios such as stock splits, public opinion surveys, delivery times, hurricane wind speeds, and others.
Sign Test for Stock SPLITS BENEFICIAL?
In evaluating whether stock splits are beneficial, the sign test is applied to a sample where 15 out of 20 stock splits resulted in an increase, 3 in a decrease, and 2 no change. The hypotheses are:
- Null hypothesis (H0): The median effect of stock splits on investment value is zero (no benefit).
- Alternative hypothesis (H1): The median effect is positive, indicating benefit.
At significance level α = .01, the binomial distribution is used to determine the probability of observing at least 15 increases under H0. The result indicates strong evidence to reject H0, suggesting stock splits are beneficial to stockholders.
Public Opinion Sign Test
The 2008 survey with 600 adults recorded varying expectations for children’s future quality of life. The sign test compares the number expecting a better versus a worse life. Hypotheses:
- H0: No difference in expectations (equal number expect better and worse).
- H1: More expect a better life.
Computing the binomial probability for 240 or more expecting a better life (out of 290 who have a definite opinion), and comparing it with α = .01, suggests insufficient evidence to conclude a significant difference, as the p-value exceeds significance level.
Comparison of Delivery Times
The delivery data from two services are analyzed using the median test at a 0.10 significance level. The signs (differences) indicate whether one service is faster, and a Wilcoxon signed-rank or sign test determines if median delivery times differ significantly.
Hurricane Wind Speeds
Wind speeds in hurricanes across regions are compared to test if their distributions are statistically similar. Using the non-parametric test (e.g., Mann-Whitney U), the data analysis indicates whether wind speed distributions differ significantly at α = .10.
Additional Analysis and Conclusion
Further probability calculations involving chi-square distributions for sample standard deviations, sample size determinations based on margin of error and confidence levels, and hypothesis testing for population means and proportions, demonstrate the applicability of statistical principles. Overall, these methods enable informed decisions based on sample data across various fields, including finance, meteorology, and public opinion.
Conclusion
This paper illustrates the importance of non-parametric tests such as sign tests in analyzing median effects and differences when data do not meet parametric assumptions. Proper hypothesis formulation and significance testing allow researchers to draw valid inferences, ultimately supporting or refuting claims or hypotheses rooted in empirical data.