BUSN Flashcards
SE for mean
s/(sqrt of n)
SE for proportions
sqrt of [p(1-p)/n]
the collection of ˆy is called
sampling distribution
-it is a t-distribution
degrees of freedom
DF=n-1
-use degrees of freedom to specify how close the t-curve is to the normal curve
mean
true population mean, u
standard deviation
standard error of yˆ,
s/(sqrt of n)
SE(Y)
the average error between a sample yˆ and the true u
t curve
-also bell shaped
-longer tails than normal (z-curve)
-uncertainty in not knowing true std. dev
-wider confidence intervals
-*use t-curve to estimate the population (true) average “u”, based on the sample average yˆ
Confidence interval (proportions)
pˆ± ME
(ME= z* * SE)
Confidence intervals (means)
yˆ± ME
(ME= t* * SE)
Interpretation of CI for mean
There is 95% confidence that the true average ___ “u” is between ___ and ____
-the average is within the range
95% confidence meaning
if we took a large number of random samples, the true average would be inside 95% of these intervals
test statistic (proportion)
(pˆ - Ho )÷ SE
test statistic (mean)
(yˆ-µ) ÷ SE
t score data size
n ≥ 30
*if normal distribution sample size can be less than 30
sample size formula for means
n= ((t**s)÷(ME))ˆ2
*for large sample sizes use z instead of t
sample size formula for proportions
n= (z*/ME)ˆ2 * p(1-p)
the collection of pˆ
sampling distribution of pˆ
sample size requirements (proportion)
np≥ 10 and n(1-p) ≥ 10
95% meaning (proportion)
95% of samples will have pˆwithin two standard errors of the true p
-95% of the time, the true parameter p will be within 1.96 standard errors of the sample result pˆ
critical value
z
confidence interval interpretation (proportion)
we are 95% confident the true proportion of customers is between ____ and ____
-captures true p from the whole population
-95% of intervals is successful in capturing the true p
the more confident we want to be about capturing true p
the wider the interval needs to be
-very confident p is inside a wide interval
* too wide it won’t be useful
99% vs 90% vs 95%
- 99% is usually too wide to be useful
-90% doesn’t have a very high success rate
-95% usually provides a god compromise between not being to wide
the wider the interval
- the larger the margin of error
the margin of error (proportion)
gives the maximum error between p and pˆ for the given confidence
ME is half
the interval width
if previous studies suggest a certain value of p
then use it
if no previous p is available
use p=.5
if ho is inside the interval
we cannot reject it
-there is insufficient evidence to reject Ho
-p-value> a
if Ho is outside the interval
we can reject it
-there is sufficient evidence to reject Ho
-p-value < a
IMPLICATIONS
90% INTERVAL: a=.1
95% INTERVAL: a=.05
99% INTERVAL: a=.01
Small p-value e.g .002
-sufficient evidence to reject Ho
-sufficient evidence to conclude Ha
-Ho-value is OUTSIDE confidence interval
large p-value e.g .36
-Insufficient evidence to reject Ho
-Insufficient evidence to conclude Ha
-Ho value is INSIDE confidence interval
Large test statistic e.g 2 or 3 (proportion)
-pˆ is far from p
-strong evidence in favor of Ha
-likely reject H0
p-value < a
-sufficient evidence to conclude Ha (Reject Ho)
p-value > a
insufficient evidence to conclude Ha (DONT reject Ho)
Significance level
a is a value used as a cutoff for deciding how small a p value needs to be to provide convincing evidence against Ha
Small p-value
large test statistic
pˆ very far from p
p is low Ho must go
Large p-value
small test statistic
pˆ reasonably close to p
if the p is high, Ho survive
Type 1 error
Ho is TRUE, but we choose Ha
can be reduced using a=.01 (make it harder to reject Ho)
type 1: the first listed (1: Ho) is TRUE
Type 2 error
Ha is true, but we choose Ho
can be reduced using a=.10 (make easier to reject Ho)
Type 2: the second listed (2: Ha) is TRUE
