Final answer:
A 95% and 99% level of statistical significance relate to the probability of committing a Type I error and correspond to how far a value lies from the mean in terms of standard deviations – approximately 95% of values lie within two standard deviations, and over 99% lie within three. These levels are used to determine if we should reject the null hypothesis in a hypothesis test.
Step-by-step explanation:
A 95% and a 99% level of statistical significance mean that there is a 5% and a 1% chance, respectively, of committing a Type I error when the null hypothesis is actually true. In terms of standard deviation, these percentages relate to the number of standard deviations away from the mean a data point must be to be considered statistically significant. For data with a normal distribution, about 95% of the values lie within two standard deviations of the mean, while more than 99% lie within three standard deviations.
When you conduct an appropriate hypothesis test assuming all distributions are normal, the population standard deviations are roughly equal, and data were collected randomly, you use these levels of significance to determine your conclusion. A 5 percent significance level represents a 95% confidence level, meaning you would expect any observed effect to occur by chance only 5% of the time.
Hypotheses and Drawing Conclusions:
- The null hypothesis typically states that there is no effect or no difference, and the alternative hypothesis suggests there is an effect or a difference.
- The decision to reject the null hypothesis or not depends on where the test statistic falls in relation to the critical value that corresponds to the significance level.
To visualize this, you might draw a bell-shaped curve representing a normal distribution. The tails on either end of the curve show the regions beyond which data would be considered statistically significant. For a 95% confidence level, the tails contain 2.5% each, while for a 99% confidence level, each tail would contain 0.5% of the data.
Using the information provided, if we calculate a p-value that is lower than the chosen significance level (0.05 for 95% confidence, 0.01 for 99% confidence), we would reject the null hypothesis, concluding there is a statistically significant difference.