Q1. Two postmen deliver mail to similar locations. Over a 44-day period, Postman A delivers
mail to an average of 21.4 homes per day, with a standard deviation of 4.6 homes. Postman B
delivers mail at an average of 19.1 homes per day with a standard deviation of 5.1 homes, in a
period of 42 days. In general, are the means for the number of visits per day for both postmen
the same, or not? (a) Test with α = 0.05. (b) Test with α = 0.02. (c) What is the P-value?
Q2) In another region of Russia 14 out of 63 people have green eyes. Is the proportion there
0.3 ? Use a significance of 0.10 to decide.
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Q3. Radiation measurements on a sample of 45 cellular phones produced a sample mean of
0.28 and standard deviation of 0.12.
(a) Determine a 98% confidence interval for the mean radiation.
(b) A researcher claims that the average radiation for cellular phones is above 0.25. Test this
claim at α = 0.05.
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Q4) Some students believe that he is late more than 30% of the time. They count how many
times he was late for the next 36 lectures; he was late 14 times. Are these students correct?
Formulate your answer using the P-value.
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Q5)Duygu is a researcher working on sleeping patterns of adults. The average sleeping time
for a sample of 12 adults in the 20-30 age group is 8 hours, with standard deviation of 0.8
hours. The figures for a sample of 10 adults in the 30-40 age group is an average of 7.5 hours,
with a standard deviation of 1 hour.
a) Duygu claims that in general the adults in the 20-30 age group sleep more than those in the
30-40 group. Is she correct? Use α = 0.025.
b) Find the 98 % confidence interval for the difference in the mean sleeping times between
the 20-30 age group and the 30-40 age group
c) Repeat parts (a) and (b) if all numbers for sample averages and standard deviations remain
the same, but sample sizes for the 20-30 age group is 42 instead of 12, and for the 30-40 age
group is 40 instead of 10.
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Q6)Two processes in a manufacturing line are performed manually: operation A and
operation B. A random sample of 50 assembly times for operation A has an average of 8.35
minutes, with a standard deviation of 1.36 minutes. A random sample of 28 assembly times
for operation B has an average of 7.53 minutes, with a standard deviation of 1.06 minutes.
a) What is the point estimate, error margin, and estimated standard error for the 99%
confidence interval for mean assembly time for operation A?
b) Is the mean assembly time for operation B less than 8 minutes? Test with confidence 0.025.
c) What is the P-value in part (b)?
d) Is the mean assembly time for operation A more than 8 minutes? Test with   0.025 .
e) Is the mean assembly time for operation A more than 8 minutes if the sample standard
deviation is 1.06 instead of 1.36? Find the P-value and comment.
Bonus: What is the probability that the difference of the sample averages for the two
operations is more than 0.82 if we assume that the mean assembly times for both operations
are the same? (Assume that the sample sizes of 50 and 28 allow you to use large sample
methods)
Q7)Mr. Sea Stayman is the leader of the Social Equality Party (SEP). The SEP conducts a
poll among 435 randomly chosen voters, and 112 of these say that they will vote for the SEP.
At the same time, the rival National Front Party (NFP) also conducts a poll among 265
randomly chosen voters, and 48 of these say that they will vote for the NFP.
a) Is the percentage of voters who will vote for the SEP in the next elections more than 21.5%?
Test with significance 0.025.
b) What is the P-value for the test in part (a)?
c) Mr. Stayman thinks that his party will get a higher proportion of the votes than the NFP. Is
he right? Test with significance 0.01.
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Q8)
a) H 0 :   3 , H1 :   3 ; with N = 120, s = 2.48, P-value: 0.0120
What is X ?
b) H 0 : 1   2  0 , H1 : 1   2  0 ,   0.01
N1  18 , N 2  14 , s1  1.1 , s2  0.8 , X  8.2
If Tsc  2.5 , what is Y ? Do we reject H 0 ?
d) H 0 :   14 , H1 :   14 ; with N = 12, s = 2.4, X = 15.5249
Find the P-value.
e) In a sample of N = 120, 55 have the characteristic. Based on this sample, test with
  0.025 whether the proportion of this characteristic in the population is more than 0.4.
f) H 0 :   4 , H1 :   4 ; with N = 12, X  4.2 , s = 1.1
If   0.05 , do we reject H 0 ?
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Q9)
a) The hypothesis test H 0 :   A vs. H1 :   A with   B results in the question
3.22  3
“ Is
> 2.06 ? ”
1.2 / 12
What is A, B, N , X , and s ?
A
B
N
X
s
b) The hypothesis test H 0 :   A vs. H1 :   A with   B results in the question
4.5  4
 1.761 ? “
“ Is  1.761 
1.1 / 3.873
What is A, B, N , X , and s ?
A
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B
N
X
s
Q10) You sample with size N from a normal population and want to test
H 0 :   12 vs. H1 :   12 . What is the P-value of the test if
a) X  12.623 , s  1.25 , and N = 25.
b) X  12.5 , s  1.25 , and N = 36.
c) X  12.6 , N = 25, and  is known to be 1.25
Answers: (a) _________________ (b) __________________ (c) __________________
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Q11) Test the null hypothesis H 0 : 1   2  0 against the alternate hypothesis
H1 : 1   2  0 with   0.01 if two normal populations with equal standard deviations
were sampled with
N1  18 and N 2  14 . The sample average and standard deviation of the first population is 8.2
and 1.1, respectively, and the sample average and standard deviation of the second population
is 7.34 and 0.8, respectively.
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Q12)
a) You want to test H 0 :   3 against H1 :   3 , and you sample from the population with
N  144 (you can thus assume that   s ). If the sample standard deviation is 1.2, and the Pvalue is 0.0125, what is the sample mean?
b) You want to test H 0 :   12 against H1  12 . If you sample from the population with
N  25 , and obtain X  12.623 and s  1.25 , what is the P-value?
c) You sample with N  15 from a population, and obtain X  4.5 and s  1.1 . If you
perform the test H 0 :   4 against H1 :   4 , do you reject H 0 at significance level
  0.1?
d) It is thought that one-ninth (1/9) of the people of Linksland are left-handed. A noted
educator claims that this proportion is higher. An university research team tests 648 randomly
chosen people, and 91 are found to be left-handed. What is the P-value of the test?