Question

A random sample of 10 measurements on the breaking strength of a certain type of material has a variance 3.21 psi2 . Repeated measurements on a second machine with 9 measurements shows a variance 2.32 psi2 . Assuming that the measurements are normally distributed, what is the ratio between the two variances at the 95% confidence level?

Answer #1

Past experience has indicated that the breaking strength of yarn
used in manufacturing drapery material is normally distributed and
that σ = 8.7 psi. A random sample of nine specimens is tested, and
the average breaking strength is found to be 86.5 psi. The 95%
confidence interval for the true mean breaking strength is written
as (A ; B). Find the value of A? round your answer to three
digits.

For a random sample of 50 measurements of the breaking strength
of Brand A cotton threads, sample mean ¯x1 = 210 grams,
sample standard deviation s1 = 8 grams. For Brand B,
from a random sample of 50, sample mean ¯x2 = 200 grams
and sample standard deviation s2 = 25 grams. Assume that
population distributions are approximately normal with unequal
variances. Answer the following questions 1 through 3.
1. What is the (estimated) standard error of difference between
two...

Two types of plastics are suitable for use by an electronics
component manufacturer. The breaking strength of these plastics is
very important. From a random sample size of n1=18, and
n2=16, we obtained that X1-bar=151.2,
S1=1.4 and X2-bar=152.3,
S2=1.65.
Calculate a 95% confidence interval on the ratio of
variances.
With 95% confidence, what is the left-value of the two-sided
confidence interval on the ratio of variances?
Your Answer:

Two types of plastics are suitable for use by an electronics
component manufacturer. The breaking strength of these plastics is
very important. From a random sample size of n1=18, and
n2=16, we obtained that X1-bar=151.2,
S1=1.4 and X2-bar=152.3,
S2=1.65.
Calculate a 95% confidence interval on the ratio of
variances.
With 95% confidence, what is the right-value of the two-sided
confidence interval on the ratio of variances?
Your Answer:

Two types of plastics are suitable for use by an electronics
component manufacturer. The breaking strength of these plastics is
very important. From a random sample size of n1=18, and
n2=16, we obtained that X1-bar=151.2,
S1=1.4 and X2-bar=152.3,
S2=1.65.
Calculate a 95% confidence interval on the difference in
means, assuming that the population variances are equal.
With 95% confidence, what is the left-value of the two-sided
confidence interval on the difference in means?
Your Answer:

Suppose the breaking strength of plastic bags is a Gaussian
random variable. Bags from company 1 have a mean strength of 8
kilograms and a variance of 1 kg2 ; Bags from company 2 have a mean
strength of 9 kilograms and a variance of 0.5 kg2 . Assume we check
the sample mean ?̅ 10 of the breaking strength of 10 bags, and use
?̅ 10 to determine whether a batch of bags comes from company 1
(null hypothesis...

Exercise 1. The sound intensity of a certain type of food
processor in normally distributed with standard deviation of 2.9
decibels. If the measurements of the sound intensity of a random
sample of 9 such food processors showed a sample mean of 50.3
decibels, find a 95% confidence interval estimate of the (true,
unknown) mean sound intensity of all food processors of this
type.
Exercise 2. What is the answer to Exercise 1 if the standard
deviation of the population...

The working life (in years) of a certain type of machines is an
exponential random variable with parameter λ, which depends on the
quality of its chip. Suppose that the quality of chips are random
in a sense that λ is uniformly distributed between [0.5, 1].
1.Find the expected working life of a machine.
2.Find the variance of the working time of a machine.

A random sample of n measurements was selected from a population
with unknown mean mu and standard deviation sigmaequals30 for each
of the situations in parts a through d. Calculate a 95% confidence
interval for mu for each of these situations.
a. nequals50, x overbarequals22
b. nequals250, x overbarequals108
c. nequals110, x overbarequals17
d. nequals110, x overbarequals4.25
e. Is the assumption that the underlying population of
measurements is normally distributed necessary to ensure the
validity of the confidence intervals in...

1. The breaking strengths (measured in dynes) of nylon fibers
are normally distributed with a
mean of 12,500 and a variance of 202,500.
a) What is the probability that a fiber strength is more than
13,175?
b) What is the probability that a fiber strength is less than
11,600?
c) What is the probability that a fiber strength is between 12,284
and 15,200?
d) What is the 90 th percentile of the fiber breaking strength?
2.
Suppose that X, Y...

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