PSYC2009 Study Guide - Quiz Guide: Type I And Type Ii Errors, Confidence Interval, Null Hypothesis
Confidence Intervals and Significance Tests
Parameter estimation for a mean
• Any sample mean (X̅) can be related to the population mean it is generated from as a
combination of the population mean () and some sampling error (e)
o
Confidence interval for a mean
• Sampling distributions (like t-distribution and normal distribution) represent how sample
mean vary around the population mean
• Confidence interval gives a range of values which contain a certain percentage of this sample
distribution
• Percentage is the confidence level
• To calculate the confidence interval for a mean:
o Confidence level
o Sample size: N
o Sample mean: X̅
o Sample standard deviation: s
o Sampling distributions of the sample mean
Calculating the confidence interval of a mean
1. Calculate standard error "SX̅". This is the standard deviation of the sampling distribution
o
2. Find the critical t-value for a two tailed t-test
. This is the value that cuts the top and bottom
from the
from t-distribution, where
o Use table (A.3, at back of textbook, or table for t-values can be found online) to find the
cell corresponding to , and the column for the two trailed test with the
value of
3. Calculate the half-width, w. this translates the critical t-value into terms of our original scale
o
4. Generate confidence interval
o
• Null hypothesis = H, alternative hypothesis = H
• Significance testing: values inside the confidence interval are said to be "plausible" values of
the unknown population parameter, while values outside a confidence interval are said to be
"implausible"
o At the specified ;level of confidence, we can reject any hypothesis where all values are
implausible, and we fail to reject a hypothesis with any plausible values
Type I and Type II Error
1. Type I error (and confidence)
o Type I error is the probability that the null hypothesis is incorrectly rejected. In others
words, we rejected but its actually true. It defined by and so we can find type I
error by finding:
•
o From this we can determine that type I error probability decreases as confidence level
increases.
2. Type II (and power)
o Type II error is the probability that the null hypothesis is not rejected when it should be.
In other words, we fail to reject but it's actually false
• It is defined by
• Probability of correctly rejecting the null hypothesis is called the power of a test
and is determined by:
▪
find more resources at oneclass.com
find more resources at oneclass.com
