L4 Flashcards
Confidence interval
- an estimated range (Interval) which includes the population parameter with high probability (confidence) based on the sample
are narrower of wider confidence intervals more informative?
narrower confidence intervals.
–> holding other things constant, more data imply narrower confidence intervals
What is the complement of the rejection region in a two-tailed test with the significance level alpha
the confidence interval
What has to be known for the Z-test to estimate the CI for the population mean?
The standard deviation or population variance
Which test is conducted to find the CI when the population standard deviation is unknown?
the T-test; to test whether the population mean u equals to a specific value when population SD is unknown
How do we get the T-statistic?
We replace population SD in the Z-formula by s (SD for sample)
t-statistic?
t=(x-u)/(s/sqrt(n))
How does the T or Z test work? The logic behind the formula?
Compare the observed to the expected value relative to the standard error (SE):
(Observed-Expected) / SE
What is the standard error?
The standard error (SE) of a statistic is the standard deviation of its sampling distribution.
Mathematically, the variance of the sampling distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean.
What does the T distribution approach when v (degrees of freedom) increase?
The standard normal distribution
Which test statistic is used when we make inference about a population variance?
- the test statistic Chi-squared will be used
Do the critical values of a two-tail test have to be calculated separately for the chi-squared distribution?
Yes because it is not symmetrical
Is the Chi squared test on the population variance sensitive to departures from normality?
Yes, if the underlying population is skewed, the actual type 1 error rate will be larger than assumed
When are the Z- and T-tests applicable?
When the variable of interest is interval (numerical)
Which type of inference are we interested in with nominal or ordinal variables?
About the population proportion
