Ch 17 - Inference for a population mean (σ unknown) Flashcards
When σ is unknown The ____ provides an estimate of the population standard deviation σ.
sample standard deviation s
___ give more reliable estimates of σ.
Larger samples
When σ is estimated from the sample standard deviation s, the statistic follows the __ distribution, symmetric about ___, with ___degrees of freedom.
t
0
n − 1
When n is very large, s is
a very good estimate of σ and the corresponding t distributions are very close to the Normal distribution.
The t distributions become wider for ___, reflecting the ___
smaller sample sizes
lack of precision in estimating σ from s.
T distribution vs normal distribution
t - more area in tails
standard error of the mean
SEM
s/√n
For a sample of size n,the sample standard deviation s is:
Table C shows the z-values and t-values corresponding to ____
When σ is unknown we use ___
When σ is known, we use ___
landmark P-values/ confidence levels.
unknown - dof
known - z value
When σ is estimated from s, the distribution of the test statistic t is a ____
This resulting t test is robust to deviations from Normality as long as ___
t distribution with df = n – 1.
the sample size is large enough.
The P-value is
the probability, if H0 was true, of randomly drawing a sample like the one obtained or more extreme in the direction of Ha
same as before
How to extiamate t using the C table
For Ha: μ > μ0
if n = 10 and t = 2.70, then
Is there evidence that storage results in sweetness loss for the new cola recipe at the 0.05 level of significance (a = 5%)?
A confidence interval is a
range of values that contains the true population parameter with probability (confidence level) C.
how to find the margin of error with both u and σ unknown
What is the true population mean sweetness loss after storage? We want 90% confidence.
Matched pairs t procedures
to compare treatments or conditions at the individual level - NOT independent
Using people matched for age, sex, and education in social studies allows us to
cancel out the effect of these potential lurking variables.
variable studied in Matched pairs t procedures become
The t procedures are exactly correct when
the population is exactly Normal.
This is rare.
The t procedures are robust to small deviations from Normality, but:
When n < 15, the data must be close to Normal and without outliers.
When 15 > n > 40, mild skewness is acceptable, but not outliers.
When n > 40, the t statistic will be valid even with strong skewness.
