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Yukon College course MATH 105 (Intro Stats) blackboards
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March 1 Boards
This document discusses statistical techniques for comparing two sample means, including calculating a confidence interval for the difference between two means to determine if they could be the same or different, and provides examples of how to perform these calculations and interpret the results.
Boards March15 17
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Monday January 11
This document discusses various statistical methods for analyzing paint data from two brands, including calculating the mean, median, mode, variance, and standard deviation using both the table method and shortcut method. It also discusses how the mean, median and mode differ for symmetric versus skewed distributions.
Jan13 Boards
Chebyshev's theorem states that at least 1-1/k^2 of data is within k standard deviations of the mean, no matter the distribution. The document discusses calculating z-scores, percentiles, standard deviation, and using a 5-number summary to create a boxplot comparing the variability in heights of the tallest buildings in New York and Hong Kong.
February 17 Blackboards
The document discusses confidence intervals for means and proportions. It provides formulas for calculating confidence intervals for a mean when sample sizes are both larger and smaller than 30, and the population standard deviation is both known and unknown. It also provides the formula for calculating a confidence interval for a sample proportion when the sample size is large enough. Examples are given of finding confidence intervals for means, proportions, variances, and standard deviations. The margin of error is defined as half the width of the confidence interval.
Recommended
March 1 Boards
This document discusses statistical techniques for comparing two sample means, including calculating a confidence interval for the difference between two means to determine if they could be the same or different, and provides examples of how to perform these calculations and interpret the results.
Boards March15 17
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Monday January 11
This document discusses various statistical methods for analyzing paint data from two brands, including calculating the mean, median, mode, variance, and standard deviation using both the table method and shortcut method. It also discusses how the mean, median and mode differ for symmetric versus skewed distributions.
Jan13 Boards
Chebyshev's theorem states that at least 1-1/k^2 of data is within k standard deviations of the mean, no matter the distribution. The document discusses calculating z-scores, percentiles, standard deviation, and using a 5-number summary to create a boxplot comparing the variability in heights of the tallest buildings in New York and Hong Kong.
February 17 Blackboards
The document discusses confidence intervals for means and proportions. It provides formulas for calculating confidence intervals for a mean when sample sizes are both larger and smaller than 30, and the population standard deviation is both known and unknown. It also provides the formula for calculating a confidence interval for a sample proportion when the sample size is large enough. Examples are given of finding confidence intervals for means, proportions, variances, and standard deviations. The margin of error is defined as half the width of the confidence interval.
March 3 Boards
This document discusses statistical tests for small sample sizes and compares means and proportions. It explains that for samples less than 30, the standard deviations must first be tested for equality before selecting the appropriate t-test to compare means. It also describes finding the average difference of paired samples and computing a weighted estimate of population proportion when comparing two proportions from small samples.
February 24 Blackboards
This document provides examples of statistical hypothesis tests including small sample tests with unknown standard deviation, tests on proportions, chi-squared tests for standard deviation that can be one-tailed or two-tailed, examples of right-tailed and left-tailed tests for standard deviation, and an example of using a confidence interval to test a hypothesis. It includes examples of each type of test.
February 22 Blackboards
The document discusses hypothesis testing and outlines several key steps and concepts:
1) It introduces the concept of determining how likely the sample mean (X-bar) is if the null hypothesis that the sampling distribution is centered on a particular value (mu) is true.
2) It notes that either the null hypothesis or alternative hypothesis could be claimed and that the null is assumed true unless evidence suggests otherwise.
3) Examples are provided to illustrate the traditional method and P-value method of hypothesis testing and their steps.
4) It emphasizes that there is always a chance of making a Type 1 error in hypothesis testing and outlines strategies for one-tailed vs two-tailed tests.
February 3 Blackboards
This document introduces the concept of sampling distributions of sample means and provides examples of constructing these distributions. It demonstrates using normal distributions to approximate probabilities for sampling distributions and the binomial distribution when sample sizes are large. Notational errors are noted regarding using X-bar minus mu-sub-X-bar instead of mu-sub-X-bar minus mu in the calculation of z-scores for these distributions.
January 27 Boards
The document discusses the binomial distribution formula for calculating the probability of getting X heads out of n coin flips. It notes that X heads can occur in different orders, so the probabilities of each arrangement must be combined using combinations. The binomial distribution accounts for all possible arrangements of getting X heads out of n trials.
January 25 Boards
The document discusses a tree diagram showing the possible outcomes of flipping a coin 3 times and the probability distribution of heads. It also discusses statistics from a survey including the mean number of credit cards owned and standard deviation. Finally, it compares the expected values of two bonds, concluding that Bond X has a better expected value than Bond Y, making it the better investment given its risk and reward.
January 20 Blackboards
To pick a team of 3 people out of 5 in a particular order, we use the fundamental counting rule which states that the number of possible sequences is equal to the number of choices at each step multiplied together. In this case, for the first pick there are 5 options, for the second there are 4, and for the third there are 3, so by multiplying these together (5 * 4 * 3 = 60) there are 60 possible teams of 3 that can be selected from 5 people in a particular order.
January 18 Blackboards
The document discusses probability concepts like sample spaces, empirical probabilities, addition rules for mutually exclusive and non-mutually exclusive events. It provides examples using data on prison sentences, endangered species, and classical probability to illustrate computing probabilities for mutually exclusive events by addition and accounting for overlap when events are not mutually exclusive.
Friday January 8
This document discusses various types of graphs that can be used to visualize different types of data including: a histogram to show the frequency distribution, a frequency polygon drawn over a histogram, an ogive, a Pareto chart of blood type data, a time series graph, a pie chart of blood type data, and a stem-and-leaf plot of protein data columns.
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March 3 Boards
This document discusses statistical tests for small sample sizes and compares means and proportions. It explains that for samples less than 30, the standard deviations must first be tested for equality before selecting the appropriate t-test to compare means. It also describes finding the average difference of paired samples and computing a weighted estimate of population proportion when comparing two proportions from small samples.
February 24 Blackboards
This document provides examples of statistical hypothesis tests including small sample tests with unknown standard deviation, tests on proportions, chi-squared tests for standard deviation that can be one-tailed or two-tailed, examples of right-tailed and left-tailed tests for standard deviation, and an example of using a confidence interval to test a hypothesis. It includes examples of each type of test.
February 22 Blackboards
The document discusses hypothesis testing and outlines several key steps and concepts:
1) It introduces the concept of determining how likely the sample mean (X-bar) is if the null hypothesis that the sampling distribution is centered on a particular value (mu) is true.
2) It notes that either the null hypothesis or alternative hypothesis could be claimed and that the null is assumed true unless evidence suggests otherwise.
3) Examples are provided to illustrate the traditional method and P-value method of hypothesis testing and their steps.
4) It emphasizes that there is always a chance of making a Type 1 error in hypothesis testing and outlines strategies for one-tailed vs two-tailed tests.
February 3 Blackboards
This document introduces the concept of sampling distributions of sample means and provides examples of constructing these distributions. It demonstrates using normal distributions to approximate probabilities for sampling distributions and the binomial distribution when sample sizes are large. Notational errors are noted regarding using X-bar minus mu-sub-X-bar instead of mu-sub-X-bar minus mu in the calculation of z-scores for these distributions.
January 27 Boards
The document discusses the binomial distribution formula for calculating the probability of getting X heads out of n coin flips. It notes that X heads can occur in different orders, so the probabilities of each arrangement must be combined using combinations. The binomial distribution accounts for all possible arrangements of getting X heads out of n trials.
January 25 Boards
The document discusses a tree diagram showing the possible outcomes of flipping a coin 3 times and the probability distribution of heads. It also discusses statistics from a survey including the mean number of credit cards owned and standard deviation. Finally, it compares the expected values of two bonds, concluding that Bond X has a better expected value than Bond Y, making it the better investment given its risk and reward.
January 20 Blackboards
To pick a team of 3 people out of 5 in a particular order, we use the fundamental counting rule which states that the number of possible sequences is equal to the number of choices at each step multiplied together. In this case, for the first pick there are 5 options, for the second there are 4, and for the third there are 3, so by multiplying these together (5 * 4 * 3 = 60) there are 60 possible teams of 3 that can be selected from 5 people in a particular order.
January 18 Blackboards
The document discusses probability concepts like sample spaces, empirical probabilities, addition rules for mutually exclusive and non-mutually exclusive events. It provides examples using data on prison sentences, endangered species, and classical probability to illustrate computing probabilities for mutually exclusive events by addition and accounting for overlap when events are not mutually exclusive.
Friday January 8
This document discusses various types of graphs that can be used to visualize different types of data including: a histogram to show the frequency distribution, a frequency polygon drawn over a histogram, an ogive, a Pareto chart of blood type data, a time series graph, a pie chart of blood type data, and a stem-and-leaf plot of protein data columns.