Final Exam Review Problems---Procedures
#1) rank the data from low to high (place data in L1
& press STAT, go to 2 (SortA..). Count the # of data pts. If there
is an odd #, take the middle data pt. If there is an even #, take the
average of the two middle values.
#2) the mode is the most repeated data pt. (there can be more
than one, if there are several data pts repeated the same # of times
& that # is the greatest. In this example, there are two. (bimodal)
#3)..place the data in L1, then go to STAT, move to CALC, stay at 1 (1-Var Stats), Enter, 2nd L1,
Enter, at the top is the mean, then further down you'll see Sx..that's
the standard deviation, now copy it where the cursor is blinking, press
x square (5th button on left column), Enter, then you will see the
variance...it's the standard deviation squared...that's it!
#4) use the formula for finding the z score: z = (x - m)/
s. If the z score is greater than 2 or less than -2, it is
considered unusual. (more than 2 SD away from the mean).
#5)..clear your lists, then place the data in L1, you would like to put the data in order, from low to high, to do this press STAT, go to 2 (SortA..), Enter, the data in L1
should be in order now, from low to high...on your list, locate 210
& see how many scores are below it...take the # of scores below 210
& divide by the total # of scores & you'll get a
decimal...convert it to a %...& that’s it...that would the %tile score for 210...
#6) find the z scores for each case & take the largest one for the best relative position.
#7) enter the midpoints of each interval (waiting time) into L1..enter number of customers in L2..then press STAT, CALC, stay at 1 (1-VarStats), Enter...The mean will be displayed..
#8) make sure the scores are ranked from low to high (they are given this way). If not, enter them in L1
& sort them...count the # of scores...take 40% of that #. If the
result is a whole #, count to that position & average that value
with the next one. If the result has a decimal, take the next number
(count to that position & take that value).
#9)..this is a little tougher...i think there was one on one of your
quizzes but with different probabilities...use a probability tree
diagram...S at the top (Start), draw 2 stems, one for W & one for
L...(first possibility for A)...then from each, do it again (2 stems, W
or L)...Stop when you have two W's, since the match would be over. then
on each stem, place it's probability...you should have 3 different
paths....multiply the probabilities along each path for that
result...add the results for each different path...(must use fractions,
not decimals)...once you get all 3 fractions into one, that will
represent the probability that A wins...since it will be less than
one-half , it's not likely...then figure the odds against...this is one
of the hardest on the final.
NOTE: a quick way to solve this one is to figure the number of
ways A can get 2 wins out of a possible 3 games (3 games do not have to
be played).
These are WW, WLW,& LWW. Then figure the probability for each by
the multiplicaion rule. Then add the results of all 3 (since they are
mutually exclusive). Just make sure when you add fractions, the bottoms
(denominators) are all the same. Once you get the final fraction
result, that would be the probability that A wins 2 of 3 games played.
The odds can now be stated, since odds come from the probabiliy.
#10)..67 do not contain errors. Find the # ways of selecting 5 from 67, 67C5 divide this by the # of ways of selecting any 5 from 76, 76C5..Enter 67 first, then MATH, PRB, (3)combination, then 5, divide, 76, MATH, PRB, (3), 5, Enter...
#11)...this is a binomial probability problem...first of all, at least
3 means 3,4,5, or 6. P(at least 3) = 1 - P(opposite of at least 3) = 1
- P(0,1,or 2)...since this starts at 0, we can get P(0,1, or 2) using
2nd VARS, down to A (binomacdf)...just make sure of how you insert (n,
p, x)...in that order...n=6, p=.44, x=2...don't forget, that answer
must be subtracted from 1...that’s it...
NOTE: You can get the answer in one calculation by entering 1 - 2nd Vars, menu A, enter (6,.44,2).
#12) Since it is given that the
flight was on time, go to that column. (this has happen). Take the # of
Trop flights & divide by the total # of flights from that column.
#13) find the # of ways you can select 4 nonsmokers from all of
the 982 nonsmokers. Use combinations, like in #10...take this # and
divide by the # of ways you can select any 4 adults from the total in
the sample space of 1161..(again, use combinations).
#14) this is similar to #11. However, "less than 3" is already cumulative. So, go directly to 2nd, VARS, Menu A (binomalcdf). No backdoor approach is needed. Enter (n, p, r), n=10, p=.23, r=2 to find P(0,1, or 2).
#15) Another problem similar to #11...P(15 or more)=1-P(up to
14)..use same menu with n=22, p=.5, x=14, then subtract from 1.
NOTE: You can get the answer in one calculation by 1 - 2nd Vars, menu
A, enter (22,.5,14). If answer is less that .05, it would be considered
a rare event & that person would seem to have ESP...a smaller
result, would be a strong case for ESP..
#16) To find the scores that separate an area of .17 to the far
right & .17 to the far left...use 2nd VARS, (3) InvNorm(.17, 25.88,
2.37) Enter (for the left one) & symmetry for the right [or
InvNorm(.83, 25.88, 2.37) Enter].
#17) the easy way to do this is to use STAT, Tests, (A)
1-PropZint, Enter, enter in x, n, C-level, Calculate,.the interval will
be displayed...the margin of error would be the difference between the
upper value & the center value , which is displayed under the
interval...so, just find that difference..You could also do this by
formula....E = Za/2 sqr[pq/n]...but, more work is involved....Za/2 = Z.01 (use InvNorm (.99)), p =77/355, q=(355-77)/355, n=355...
#18) Use the formula in #17 for E, but split up the square root
over the top & bottom of the fraction...Then switch E with the
sqr(n)...then square the result to get n...any fractional result is
taken to the next whole #.
#19) Since the population SD (all students taking the test) is
unknown, use a T-Interval..STAT, Tests, (8) Tinterval..input the
required information...you could also use the Formula, E = (ta/2) S/sqr(n)...where ta/2 = t.005
(get this from table A-3, where area in two tails is 0.01), S is
the standard deviation of the sample of 25, n=25...then, add &
subtract this result, which is E, from the sample mean (center of the
interval)..much more work...(a similar method can be used for a Z
interval if S is replaced by the population standard deviation).
#20) Use a Z Test (pop SD is known)...STAT, Tests, (1) Z-Test where Ho is that pop mean = 25 & H1 not equal to 25..(there is no direction implied or stated)..if the p-value is less than .01, we reject Ho...
#21) Use a T Test (pop SD is unknown, sample SD, Sx is given)...Ho is mean= 13.7 & H1 is mean<13.7
...STAT, Tests, (2) T-Test...reject Ho if the p-value is < .05...
#22) go to table A-6 with the correlation given &
sample size n...look under the significance level asked for...this is
the critical value...if the absolute value (no negative sign) of your
correlation is greater than that critical value, then it is significant
at that level....it’s possible to be significant at the .05 level
but not at the .01 level, however, if it is not significant at the .05
level, it can not be significant at the .01 level...
#23) insert your data in L1 (x-values) & L2
(y-values), carefully...then go to STAT, Tests, (E) LinRegTTest...use r
not equal to, skip to Calculate, Enter....look for a &
b...then place them in the equation, y = a + bx
#24) insert your data in L1 & L2 (for correlation, it doesn’t matter which lists you use)..Go to the same menu as in #23, but look for r
#25) see if the r given in the problem is significant (use
table A-6 with n & the significance level)...if it is, substitute
the value of x into the regression equation for the best predicted
y...if it isn’t, use y average as the best predicted y (for any
x)...
~Note: Make sure you know
these procedures well...the final exam problems model the review
problems...all questions are multiple choice...