Question

Suppose the average lifetime of a certain type of car battery is known to be 60 months. Consider conducting a two-sided test on it based on a sample of size 25 from a normal distribution with a population standard deviation of 4 months.

a) If the true average lifetime is 62 months and a =0.01, what is the probability of a type II error?

b) What is the required sample size to satisfy and the type II error probability of b(62) = 0.1?

**Please type down your answer.**

Answer #1

The lifetime of a certain type of battery is known to be
normally distributed with a population standard deviation of 20
hours. A sample of 50 batteries had a mean lifetime of 120.1
hours.
a. What is the point estimate?
b. Calculate the sampling error.
c. Construct a 95% confidence interval for the population mean.
Explain the answer in a sentence.

The lifetime of a certain battery follows a normal distribution
with a mean 276 minutes and standard deviation 25 minutes. We took
a random sample of 100 of these batteries. What is the probability
that the sample mean of the lifetime will be less than 270
minutes?

The lifetime of a certain battery follows a normal distribution
with a mean 276 minutes and standard deviation 20 minutes. We took
a random sample of 100 of these batteries. What is the probability
that the sample mean of the lifetime will be less than 270
minutes?
A.0.9987
B.0.0013
C.0.4987
D.0.3821

9. The standard deviation of the lifetime of a certain type of
lightbulb is known to equal 100 hours. A sample of 169 such bulbs
had an average life of 1350 hours. Find a
(a) 90percent (b) 95percent (c) 99percent
confidence interval estimate of the mean life of this type of
bulb.

Let μ denote the mean lifetime (in hours) for a certain
type of battery under controlled laboratory conditions. A test
of
H0: μ = 10
versus
Ha: μ
< 10
will be based on a sample of size 36. Suppose that σ is
known to be 0.6, so
σx = 0.1.
The appropriate test statistic is then
z =
x − 10
0.1
(a)
What is α for the test procedure that rejects
H0
if
z ≤ −1.38?
(Round your...

A researcher wants to study the average lifetime of a certain
brand of rechargeable batteries (in hours). In testing the
hypotheses, H0: μ = 950 hours vs. H1: μ ≠ 950 hours, a random
sample of 25 rechargeable batteries is drawn from a normal
population whose standard deviation is 200 hours.
a) Calculate β, the probability of a Type II error when μ = 1000
and α = 0.10.
b) Calculate the power of the test.
Please Solve Manually.

A study of a certain brand of AA batteries yielded a sample mean
lifetime of 450 minutes with a sample standard deviation of 92
minutes. A hypothesis test was performed using the following
hypotheses: H0: μ = 480 Ha: μ < 480. A type II error for this
hypothesis test is:
a.
To conclude that the average battery lifetime is less than 480
minutes when, in reality, it is less than 480 minutes.
b.
To conclude that the average battery...

Lightbulbs of a certain type are advertised as having an average
lifetime of 750 hours. The price of these bulbs is very favorable,
so a potential customer has decided to go ahead with a purchase
arrangement unless it can be conclusively demonstrated that the
true lifetime is smaller than what is advertised. A random sample
of 60 bulbs was selected. In this sample, the mean lifetime was
741.8 and the standard deviation was 19.2. What conclusion would be
appropriate for...

A manufacturer of electronic components is interested in testing
the lifetime of a certain type of battery. A random sample of 35
observations resulted in a mean of 123 hours and a variance of 144
hours square. Does this result provide strong evidence that the
population mean is greater than 120 hours at 5% significance level
under normal distribution assumption?

Suppose that the average lifetime of a car is 100 working hours
and that the lifetime distribution is exponential.
(a) Estimate the probability that the car will work at least 50
hours.
(b) Given that the car has functioned for 50 hours, what is the
chance that it fails in the next 25 hours.
(c) Suppose that two cars, one in active, the other in reserve
(if the primary one malfunctions, the second will be used at once).
What is...

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