Question

3) The quality control department of a tire manufacturer randomly selects a number of
products from two production lines and records the results in the following table:

Durability (thousand km)
< 50	50 – 55	55 - 60	60 - 65	>= 65
Line A	7	13	30	20	10
Line B	10	15	40	9	6

a) Construct a 90% confidence interval for the difference in average durability of
products of two lines A and B.
b) At the 5% level of significance, can it be concluded that the average durability of
products between the two lines A and B is not different?
c) The director of the manufacturer declares that the manufacturer's products can be used
for at least 60,000 km. Is the statement reliable at the 5% significance level?
4) Researching the income of employees of two companies A and B, people conducted a
survey and obtained the following results: In Company A, there are 50 survey participants,
their average income is 1500 $ /month, the sample standard deviation is 138 $/month. In
Company B the corresponding figures are: 40; 1660$/month and 185 $/month.
a) At the 5% level of significance, can it be assumed that the average incomes of the
employees of two companies A and B are the same?
b) At the 3% significance level, can it be assumed that the average income of company A's
employees is not more than 1400$/month?
5) When treated with drug A, the cure rate is 80%. Changing to drug B to treat 110 people,
92 people recovered. With significance level  = 0.02 can it be said that drug B is more
effective than drug A?
6) Examining randomly products in two factories, we have the following data:

Factory	Number of products tested	Number of defective products
A	1000	20
B	900	30

a) Construct a 90% confidence interval for the difference in the proportions of defective
products between two factories A and B.
b) At the 5% significance level, can it be assumed that the percentages of defective
products of two factories A and B are the same?
7) Surveying the self-study time (hours/week) of students from Faculty A and Faculty B,
they randomly selected 100 students in each faculty and obtained the following table of
data:

self-study time	3 - 4	4 - 5	5 - 6	6 - 7	7 - 8
Faculty A	12	13	46	23	6
Faculty B	9	21	50	16	4

a) Is it possible to assume that the average number of hours of self-study for students of
the two faculties are the same at the 1% significance level?
b) There is an opinion that the percentage of students in Faculty A who self-study for less
than 4 hours/week is more than of Faculty B’s. At the 5% level of significance, please
comment on that opinion.