Applet Concept Illustrated Descriptor Applet Activity Confidence intervals for a mean Confidence intervals obtained using the sample standard deviation are different from those obtained using the population standard deviation. This applet compares the proportions of z confidence intervals and t confidence intervals that contain the mean for randomly generated samples from the same population. This applet generates confidence intervals for a population mean. The user specifies the sample size, the shape of the distribution, the population mean, the population standard deviation, and the interval type (t or z). The applet simulates selecting 100 random samples from the population and finds the 95% z- or t-interval for each sample. The confidence intervals are plotted and the number and proportion containing the true mean are reported. 6.2 Confidence intervals for a proportion This applet investigates the properties of confidence intervals for a population proportion. This applet generates confidence intervals for a population proportion. The user specifies the population proportion and the sample size. The applet simulates selecting 100 random samples from the population and finds the 95% confidence interval for each sample. The confidence intervals are plotted and the number and proportion containing the true proportion are reported. The user can input a different confidence interval for the given samples. 6.3 Hypothesis tests for a mean Not all tests of hypotheses lead correctly to either rejecting or failing to reject the null hypothesis. This applet investigates the relationship between the level of confidence and the probabilities of making Type I and Type II errors. This applet performs hypotheses tests for a population mean. The user specifies the shape of the population distribution, the population mean and standard deviation, the sample size, and the null and alternative hypotheses. The user can also adjust the confidence level. The applet simulates selecting a random sample from the population and calculates and plots the t-statistic or P-value for each sample. The applet reports the number and proportion of times the null hypothesis is rejected at the given confidence level. 7.3 Hypothesis tests for a proportion Not all tests of hypotheses lead correctly to either rejecting or failing to reject the null hypothesis. This applet investigates the relationship between the level of confidence and the probabilities of making Type I and Type II errors. This applet performs hypotheses tests for a population proportion. The user specifies the population proportion, the sample size, and the null and alternative hypotheses. The user can also adjust the confidence level. The applet simulates selecting a random sample from the population and calculates and plots the z-statistic or P-value for each sample. The applet reports the number and proportion of times the null hypothesis is rejected at the given confidence level. 7.4 Correlation by eye The correlation coefficient measures the strength of a linear relationship between two variables. This applet teaches the user how to assess the strength of a linear relationship from a scatter plot. This applet computes the correlation coefficient r for a set of bivariate data plotted on a scatter plot. The user can easily add or delete points and guess the value of r. The applet then compares the guess to its calculated value. 9.1 Regression by eye The least squares regression line has a smaller SSE than any other line that might approximate a set of bivariate data. This applet teaches the user how to approximate the location of a regression line on a scatter plot. This applet shows the y-intercept, slope, and SSE of the least squares regression line for a set of bivariate data plotted on a scatter plot. The user can easily add or delete points and guess the location of the regression line by manipulating a line provided on the scatter plot. The applet shows the y-intercept, slope, and SSE of this line. The applet will plot the least squares line. 9.2
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