Applet Correlation
| Applet | Concept Illustrated | Description | Applet Activity |
|---|---|---|---|
| Sample from a population | Assesses how well a sample represents the population and the role that sample size plays in the process. | Produces random sample from population from specified sample size and population distribution shape. Reports mean, median, and standard deviation; applet creates plot of sample. | 4.4, 192; 4.6, 207 |
| Sampling distributions | Compares means and standard deviations of distributions; assesses effect of sample size; illustrates undbiasedness. | Simulates repeatedly choosing samples of a fixed size n from a population with specified sample size, number of samples, and shape of population distribution. Applet reports means, medians, and standard deviations; creates plots for both. | 4.7, 236; 4.8, 236 |
| Random numbers | Uses a random number generator to determine the experimental units to be included in a sample. | Generates random numbers from a range of integers specified by the user. | 1.1, 19; 1.2, 20; 3.6, 159; 4.1, 178 |
| Long-run probability demonstrations illustrate the concept that theoretical probabilities are long-run experimental probabilities. | |||
| Simulating probability of rolling a 6 | Investigates relationship between theoretical and experimental probabilities of rolling 6 as number of die rolls increases. | Reports and creates frequency histogram for each outcome of each simulated roll of a fair die. Students specify number of rolls; applet calculates and plots proportion of 6s. | 3.1, 127; 3.3, 138; 3.4, 139; 3.5, 153 |
| Simulating probability of rolling a 3 or 4 | Investigates relationship between theoretical and experimental probabilities of rolling 3 or 4 as number of die rolls increases. | Reports outcome of each simulated roll of a fair die; creates frequency histogram for outcomes. Students specify number of rolls; applet calculates and plots proportion of 3s and 4s. | 3.3, 138; 3.4, 139 |
| Simulating the probability of heads: fair coin | Investigates relationship between theoretical and experimental probabilities of getting heads as number of fair coin flips increases. | Reports outcome of each fair coin flip and creates a bar graph for outcomes. Students specify number of flips; applet calculates and plots proportion of heads. | 3.2, 127; 4.2, 179 |
| Simulating probability of heads: unfair coin | Investigates relationship between theoretical and experimental probabilities of getting heads as number of unfair coin flips increases. | Reports outcome of each flip for a coin where heads is less likely to occur than tails and creates a bar graph for outcomes. Students specify number of flips; applet calculates and plots the proportion of heads. | 4.3, 192 |
| Simulating probability of heads: unfair coin | Investigates relationship between theoretical and experimental probabilities of getting heads as number of unfair coin flips increases. | Reports outcome of each flip for a coin where heads is more likely to occur than tails and creates a bar graph for outcomes. Students specify number of flips; applet calculates and plots the proportion of heads. | 4.3, 192 |
| Simulating the stock market | Theoretical probabilities are long run experimental probabilities. | Simulates stock market fluctuation. Students specify number of days; applet reports whether stock market goes up or down daily and creates a bar graph for outcomes. Calculates and plots proportion of simulated days stock market goes up. | 4.5, 192 |
| Mean versus median | Investigates how skewedness and outliers affect measures of central tendency. | Students visualize relationship between mean and median by adding and deleting data points; applet automatically updates mean and median. | 2.1, 61; 2.2, 61; 2.3, 61 |
| Standard deviation | Investigates how distribution shape and spread affect standard deviation. | Students visualize relationship between mean and standard deviation by adding and deleting data points; applet updates mean and standard deviation. | 2.4, 68; 2.5, 69; 2.6, 69; 2.7, 91 |
| Confidence intervals for a proportion | Not all confidence intervals contain the population proportion. Investigates the meaning of 95% and 99% confidence. | Simulates selecting 100 random samples from the population and finds the 95% and 99% confidence intervals for each. Students specify population proportion and sample size; applet plots confidence intervals and reports number and proportion containing true proportion. | 5.5, 279; 5.6, 280 |
| Confidence intervals for a mean (the impact of confidence level) | Not all confidence intervals contain the population mean. Investigates the meaning of 95% and 99% confidence. | Simulates selecting 100 random samples from population; finds 95% and 99% confidence intervals for each. Students specify sample size, distribution shape, and population mean and standard deviation; applet plots confidence intervals and reports number and proportion containing true mean. | 5.1, 261; 5.2, 261 |
| Confidence intervals for a mean (not knowing standard deviation) | Confidence intervals obtained using the sample standard deviation are different from those obtained using the population standard deviation. Investigates effect of not knowing the population standard deviation. | Simulates selecting 100 random samples from the population and finds the 95% z-interval and 95% t-interval for each. Students specify sample size, distribution shape, and population mean and standard deviation; applet plots confidence intervals and reports number and proportion containing true mean. | 5.3, 271; 5.4, 271 |
| Hypothesis tests for a proportion | Not all tests of hypotheses lead correctly to either rejecting or failing to reject the null hypothesis. Investigates the relationship between the level of confidence and the probabilities of making Type I and Type II errors. | Simulates selecting 100 random samples from population; calculates and plots z-statistic and P-value for each. Students specify population proportion, sample size, and null and alternative hypotheses; applet reports number and proportion of times null hypothesis is rejected at 0.05 and 0.01 levels. | 6.5, 343; 6.6, 344 |
| Hypothesis tests for a mean | Not all tests of hypotheses lead correctly to either rejecting or failing to reject the null hypothesis. Investigates the relationship between the level of confidence and the probabilities of making Type I and Type II errors. | Simulates selecting 100 random samples from population; calculates and plots t statistic and P-value for each. Students specify population distribution shape, mean, and standard deviation; sample size, and null and alternative hypotheses; applet reports number and proportion of times null hypothesis is rejected at both 0.05 and 0.01 levels. | 6.1, 317; 6.2, 327; 6.3, 327; 6.4, 327 |
| Correlation by eye | Correlation coefficient measures strength of linear relationship between two variables. Teaches user how to assess strength of a linear relationship from a scattergram. | Computes correlation coefficient r for a set of bivariate data plotted on a scattergram. Students add or delete points and guess value of r; applet compares guess to calculated value. | 9.2, 539 |
| Regression by eye | The least squares regression line has a smaller SSE than any other line that might approximate a set of bivariate data. Teaches students how to approximate the location of a regression line on a scattergram. | Computes least squares regression line for a set of bivariate data plotted on a scattergram. Students add or delete points and guess location of regression line by manipulating a line provided on the scattergram; applet plots least squares line and displays the equations and the SSEs for both lines. | 9.1, 512 |
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