Transcript AP Statistics: Section 12.1 B

AP Statistics: Section 12.1 B
Example: A bank wonders if omitting the annual credit
card fee for customers who charge at least $2400 a
year would increase the amount that customers charge
on its credit cards. The bank makes this offer to a SRS
of 200 of its credit card customers. It then compares
the amount these customers charged this year to the
amount they charged last year. The mean increase is
$332 and the standard deviation is $108.
a) Is there significant evidence at the 1% level that the
mean amount charged increases under the nofee offer?
Hypothesis:
The population of interest is credit card customers at this bank.
H0 :   0
H a :   0 where   the mean difference in
the amount of money charged on credit cards with the 2 policies.
Conditions:
SRS : Yes
Normality of x : n  200 means the CLT will give x a
distribution that is approx. Normal
Independence : No reason not to assume observations are
independent and since sampling w/o replacement N  10n
Calculations:
t
332  0
 43.474
108
200
Interpretation:
Since my p - value is less than the significance level of .01, I reject the
H 0 . I conclude that the amount charged on credit cards by this bank' s
customers increases under the no - fee plan.
b) Construct and interpret a 99% confidence interval for
the mean amount of the increase omitting the annual
credit card fee for customers who charge at least $2400
a year would increase the amount that customers
charge on its credit cards.
x t

s
108
 332  2.626
n
200
311.946,352.054
I am 99% confident that the mean increase in the amount charged
to credit cards under the banks no - fee program is between 311.946
and 352.054 dollars.
c) Does our work in parts a & b show that omitting the
annual credit card fee for customers who charge at
least $2400 a year caused an increase the amount that
customers charge on its credit cards?
NO. there could be confounding variables such as an
improvement in the economy that caused the increase.
d) Briefly describe the design of an experiment
to study the no-fee offer.
Choose a second SRS of 200 customers to use as a control group.
Compare the mean increase of the two groups.
The t procedures are robust against non-Normality of
outliers or
the population except when _________
_________________
strong skewness are present. (Skewness is more
serious than other kinds of non-Normality). Review the
guidelines in the box “Using the t-procedures” on page
655. As the sample size increases, the ______
CLT ensures
that the distribution of the sample mean becomes
more nearly Normal and the t-distribution becomes
more accurate for calculating p-values.
The power of a statistical test measures its
ability to detect deviations from the ____.
H 0 The
power of the one-sample t -test against a
specific alternative value of the population
mean  is the probability that the test will
_____________
reject the H 0 when the mean has the
alternative value.