If you have a 99% confidence interval for μμ based on a simple random sample, is it correct to say that in the long run, if you computed many, many co

Maiclubk 2021-05-09 Answered

If you have a 99% confidence interval for \(\mu;\mu\); based on a simple random sample, is it correct to say that in the long run, if you computed many, many confidence intervals using the prescribed method, about 99% of such intervals would contain \(\mu\);? Explain.

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

averes8
Answered 2021-05-10 Author has 15302 answers
Yes, because in 99% of all possible sample of sample size n, the 99% confidence interval will contain \(\displaystyle\mu\).
Not exactly what you’re looking for?
Ask My Question
3
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-08

Based on a simple random sample of 1300 college students, it is found that 299 students own a car. We wish to construct a \(\displaystyle{90}\%\) confidence interval to estimate the proportions ? of all college students who own a car.
A) Read carefully the text and provide each of the following:
The sample size \(\displaystyle?=\)
from the sample, the number of college students who own a car is \(\displaystyle?=\)
the confidence level is \(\displaystyle{C}{L}=\) \(\displaystyle\%\).
B) Find the sample proportion \(\displaystyle\hat{{?}}=\)
and \(\displaystyle\hat{{?}}={1}−\hat{{?}}=\)

asked 2021-06-01
Suppose that you take 500 simple random samples from a population and that, for each sample, you obtain a 90% confidence interval for an unknown parameter. Approximately how many of those confidence intervals will not contain the value of the unknown parameter?
asked 2021-06-24

Suppose that you have obtained data by taking a random sample from a population and that you intend to find a confidence interval for the population mean, \(\mu\). Which confidence level, 95% or 99%, will result in the confidence interval's giving a more precise estimate of \(\mu\)?

asked 2021-05-14
When σ is unknown and the sample size is \(\displaystyle{n}\geq{30}\), there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When \(\displaystyle{n}\geq{30}\), use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?
asked 2021-05-05

Consider a random sample of size n = 31, with sample mean \(\displaystyle\overline{{{x}}}={45.2}\) and sample standard deviation s = 5.3. Compute 90%, 95%, and 99% confidence intervals for \muμ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

asked 2021-08-10

A local firm manufactures LED products that have a lifespan that is approximately normally distributed with a std. dev. of 30 hours. If a sample of 30 LED products has an average lifespan of 780 hours, find a \(\displaystyle{96}\%\) confidence interval for the population mean of all LED products produced by this firm.
Choose 2 answers in nearest unit (ones) or in whole number.
Example, if your answer is \(\displaystyle{888.83}\leq\mu\leq{899.56}\), choose 889 and 900.
\(\begin{array}{|c|c|}\hline 775 & 773 & 807 & 797 & 791 & 769 & 789 & 768 & 805 & 763 & 771 & 792 \\ \hline \end{array}\)

asked 2021-05-09

The two intervals (114.4, 115.6) and (114.1, 115.9) are confidence intervals (computed using the same sample data) for \(\mu=\) true average resonance frequency (in hertz) for all tennis rackets of a certain type.
a. What is the value of the sample mean resonance frequency?
b. The confidence level for one of these intervals is 90%90%and for the other it is 99%99%. Which is which, and how can you tell?

...