Question

An electrical firm manufactures light bulbs that have a length of life that is normally distributed, with mean equal to 800 hours and a standard deviation of 40 hours. Suppose a 100 light bulbs are randomly selected for testing the length of life. Let x ̅ represent the sample mean length of life of the light bulbs.

σ_( x ̅ ) = 4 hours

n) Find a lower and an upper mean length of life of bulbs in hours such that 90% of all values of the sample mean length of life of light bulbs computed from random samples of size 100 lie in this interval.

Can you show how to do this in Rstudio?

Answer #1

R studio script

an electrical firm manufactures light bulbs that have a length
of life that is approximately normally distributed with a standard
deviation of 40 hours. the firm claims that the mean life of the
light bulb is 800 hrs
a?if a sample of 30 light bulbs were tested to failure and had
an avg life of 780 hours, find 90% confidence interval on the
mean
b) based on this confidence interval, would you be able to
validate the claimed mean life...

An electrical firm manufactures light bulbs that have a lifetime
that is approximately normally distributed with a mean of 800 hours
and a standard deviation of 40 hours. Test the claim, at the 0.05
level of significance, if a random sample of 30 bulbs has an
average life of 790 hours. Also, Find P-value

1) An electrical firm manufactures light bulbs that have a
length of life that is approximately normally distributed with a
standard deviation of 40 hours. If a sample of 36 bulbs has an
average life of 780 hours, calculate the 95% confidence interval
for the population mean of all bulbs produced by this firm
2) Is it true that the confidence interval is narrower for 95%
confidence than for 90% confidence? Explain
3) Is it true that the Sample means...

An electrical firm manufactures light bulbs that have a length
of life that is approximately normally distributed with a standard
deviation of 40 hours. If a sample of 30 bulbs has an average life
of 780 hours, construct a 96% confidence interval for the
population mean of all bulbs produced by this firm.
Identifying all the required quantities correctly from
problem statement = 5 points
Sketch the probability/ area on normal PDF curve = 5
points
Calculate the z value...

An electrical firm manufactures light bulbs that have a lifetime
that is approximately normally distributed with a mean of 800 hours
and a standard deviation of 40 hours. A researcher believes that he
can show that the average lifetime of the bulbs is greater than 800
hours, and from a random sample of 25 bulbs finds that the sample
average lifetime is 820 hours. What should the researcher conclude
about the average lifetime of the bulbs? Be sure to state...

A company manufactures light bulbs. The company wants the bulbs
to have a mean life span of 999 hours. This average is maintained
by periodically testing random samples of 25 light bulbs. If the
t-value falls between minus−t 0.95 and t 0.95 then the company will
be satisfied that it is manufacturing acceptable light bulbs. For a
random sample, the mean life span of the sample is 1006 hours and
the standard deviation is 22 hours. Assume that life spans...

A company manufactures light bulbs. The company wants the bulbs
to have a mean life span of 990 hours. This average is maintained
by periodically testing random samples of 16 light bulbs. If the
t-value falls between minus t 0.99 and t 0.99, then the company
will be satisfied that it is manufacturing acceptable light bulbs.
For a random sample, the mean life span of the sample is 1007
hours and the standard deviation is 28 hours. Assume that life...

A company manufactures light bulbs. The company wants the bulbs
to have a mean life span of
999999
hours. This average is maintained by periodically testing random
samples of
2525
light bulbs. If the t-value falls between
minus−t 0.95t0.95
and
t 0.95t0.95,
then the company will be satisfied that it is manufacturing
acceptable light bulbs. For a random sample, the mean life span of
the sample is
10061006
hours and the standard deviation is
2222
hours. Assume that life spans...

An electrical firm manufacturers light bulbs that have a length
of life approximately normal with a mean 5000 and a standard
deviation of 120 hours. To test the hypothesis that µ 5000 against
the alternative that µ < 5000 a random sample of 50 bulbs was
tested. Find the probability of committing a type II error if µ is
in fact shifted to 4950 and α = 0.05.
The probability of committing a type II error?

Question: Light bulbs have lifetimes that are known to be
approximately normally distributed.
Suppose a random sample of 35 light bulbs was tested, and =
943 hours and s = 33 hours.
a. Find a 90% confidence interval for the true mean life of a
light bulb.
b. Find a 95% lower confidence limit for the true mean life of
a light bulb.
c. Are the results obtained in (a) and (b) the same or
different? Explain why.

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