Download Homework Chapter 9—10

Homework Chapter 9—10
1. A soft drink company has a machine that is used to fill bottles of the company’s
product. A sample of 36 different cans is taken and the average amount of the product
put into the cans is measured. The results are s  0.11 oz. and x  12.19 oz. A manager
claims that the average fill of all bottles exceeds the company’s standard of 12 oz. Thus
lowering profits. Test the manager’s claim using a 0.01 level of significance. Do by
hand.
2. Work problem 1 again this time using Excel and the p-value.
P
1.57102E-12 = TDIST(10.383 ,35 ,1)
3. A physician has decided to test the claim that the mean body temperature of
healthy adults is 98.6o F . To test this claim she records the temperatures of 106
patients during their physical exams. The sample results are that the mean is
98.20 degrees and a standard deviation of 0.62 degrees. Test the claim using a
0.02 level of significance. Show all hand calculations.
4. Work problem 3 using Excel and the p—value.
P
1.38598E-09 = TDIST(6.645, 105, 2)
5. Prior to the use of electronic scanners in grocery store checkout lines humans
were responsible for entering price information into the checkout cash registers.
Because humans are involved there are always errors. Extensive research showed
that there was a 1% chance that a customer would be the victim of an overcharge
on an item. A company wishes to see if scanners reduce the probability of an
overcharge. The company finds that 20 items from a sample of 1234 items
scanned resulted in on overcharge. Based on these results, does it appear that the
scanners reduce overcharges? Test using a 5% level of significance.
6. As usual do 5 with Excel and p—values
P
0.986585657 = NORMDIST(2.214,0, 1, TRUE)
7. IQ scores have mean = 100 and standard deviation =15. You might wonder how that
could be. The people that design the exam give prototype exams to test groups. If the
results are different than those just mentioned some questions are replaced with new
questions, the exam is retested, and the process repeated until the desired mean and
standard deviation is are obtained. The results a one test group of 60 people is a sample
standard deviation of 13. Based on this result, does it seem likely that the desired
standard deviation of 15 has been obtained. Test using a 0.01 level of significance. Use
Excel and p—values.
P
0.077416 = 1 - CHIDIST(44.3, 59)
8. A restaurant manager wonders if the name of dishes affects whether the customer
decides to order the dish. He has three menus prepared giving the same dish different
names: Captain Ahab’s Delight, Seafood Ecstasy, and Whale Blubber. The number of
times customers order the dish is given in the table below. Use the ANOVA table to
determine is there is a difference in the average number of times the dish is ordered. Test
using a 0.01 level of significance.
Captain Ahab's Delight
Seafood Ecstasy
Whale Blubber.
15
14
7
15
15
8
16
16
12
Number of dinner orders per night
SUMMARY
Groups
Captain Ahab's Delight
Seafood Ecstasy
Whale Blubber.
Count
Sum
3
3
3
ANOVA
Source of Variation
Between Groups
Within Groups
SS
76.22222
16.66667
Total
92.88889
df
Average Variance
46 15.33333 0.333333
45
15
1
27
9
7
MS
2 38.11111
6 2.777778
8
F
P-value
F crit
13.72 0.005776 5.143249
10. A company is conducting a study of the salary structure of various departments. The
results of the samples from two large departments is given below
Accounting Department Engineering Department
x  77, 250
x  79, 212
s  6241
s  5356
n=150
n=100
Test
to determine if the variance in salaries is different between the two departments. Use
Excel, p—values and a 0.02 level of significance.
H 0 :  12   22
(The variance in salries is the same in both departments)
H A :  
(The variance is not the same)
2
1
2
2
 =0.02
s1  6241, s 2  5356
n1  150, df1 = 149, n2  100, df 2  99
s1=
s2=
F=
P/2
6241
5356
1.357773 = (6241*6241) / (5356*5356)
0.05133 = FDIST (1.35773, 149, 99)