Practice Problems for two sample hypothesis tests
1. A company that manufactures guitar picks in two shifts. Production supervisor Vinny
Pickman must keep tabs on both departments making sure that the number of defectives is
not particularly higher or lower in either shift. Each month he chooses a random sample
of days and counts the number of defects. Last month the morning shift averaged 10
defects with a standard deviation of 5 defects in a sample of 30 days. The evening shift,
in a sample of 30 days averaged 18 defects with a standard deviation of 6 defects. Should
Vinny schedule a reprimand for one of the shift supervisors? Explain your answer.
2. A company that manufactures guitar picks in two shifts. Production supervisor Vinny
Pickman must keep tabs on both departments making sure that the number of defectives is
not particularly higher or lower in either shift. Each month he chooses a random sample
of days and counts the number of defects. His employees don’t think it is fair to count
defects because the number of picks produced differs between shifts. Vinny, understands
their complaint and changes his system. Last month the morning shift had 100 defective
picks in a sample1000 picks. The evening shift, in a sample of 800 picks had 120 defects.
Should Vinny schedule a reprimand for one of the shift supervisors? Explain your answer.
3. A company sells tennis racquets, and is considering decreasing the price at several
stores. For the randomly selected stores the table below reflects the number of racquets
sold in the week before and the week after a price decrease
Store Location
Before
Rockbille
100
Wentby
80
Kipgoin
70
Sandyville
100
Tommytown
50
Can we be sure the price decrease worked?
After
120
85
90
110
55
4. One bright McDonalds executive suggested that perhaps there are regional differences
in pickle preference. To test his idea he checked pickle removal in east and west coast
locations. On the west coast 73 percent of 100 customers removed the pickle, while on the
east coast only 63 percent of 60 customers removed the pickle. Can we be reasonably sure
the regions differ?
5. To investigate the cost side of the pickle debate, McDonalds has run a test to see if the
average cost per sandwich is less without the pickle. (It’s cheaper to produce the burger
without the pickle, but when people request pickles cost increases dramatically because
special arrangements have to be made. At several test stores 400 sandwiches with pickles
cost an average of $.59 to make with a standard deviation of $.28. At another batch of
test stores, 500 sandwiches without pickles cost an average of $.57 to make with a
standard deviation of $.38. Can we be reasonably sure that the sandwiches without pickles
cost less to produce?
6. In a separate matter regarding sesame seed buns, a new baker claims that he can provide
an equivalent bun with more seeds for the same price. He has sent a sample of 61 buns for
McDonald's to test. In the new baker's sample each bun has an average of 140 sesame
seeds (with a standard deviation of 30 seeds). Forty-one buns from the current baker
averaged only 130 seeds (with a standard deviation of 20 seeds). Assuming that the
number of seeds is the deciding factor in the decision, should McDonalds switch buns?
7. A study is undertaken with the following results: Each patient rates their pain on a scale
of one to ten both before and after hypnosis. If there is significant evidence of the benefits
of hypnosis, more research will be undertaken. If not, the program will be dropped.
Patient A
B
C
D
E
F
G
H
Before 6.6
6.5
9.0
10.3
11.3
8.1
6.3
11.6
After
2.4
7.4
8.5
8.1
6.1
3.4
2.0
6.8
Should research continue? Explain why or why not.
8. Pennsylvania is considering increasing public school funding to keep pace with private
schools. This would mean committing millions of additional dollars to the system. This
should only happen if performance on SAT scores is significantly lower in public schools.
In a random sample of one hundred public school students, the average SAT score was
950 with a standard deviation of 200 points. In a random sample of sixty-four private
school students the average was 1000 with a standard deviation of 50 points. Should the
state increase funding to public schools?
9. There is a house in New Orleans (it’s called the Rising Sun). Supposedly the gambling
games there pay off better than the casinos in Las Vegas. Vegas claims that their casinos
pay off more than anywhere else on the planet. In Vegas, a sample of 49 gamblers lost an
average of $50 each night with a standard deviation of $50. In a sample of 36 Rising Sun
Gamblers, the average loss was $30 with a standard deviation of $25. Does either place
deserve its reputation? Explain your answer.