Decresing the sample size, while holding the confidence level and the variance the same, will do what to the length of wour confidence interval?

kuCAu 2020-11-02 Answered
Decresing the sample size, while holding the confidence level and the variance the same, will do what to the length of wour confidence interval?
You can still ask an expert for help

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

Talisha
Answered 2020-11-03 Author has 93 answers
Confidence Interval :
A confidence interval is an estimate of the population proportion, e.g, population mean, and proportion. It provides lower and upper values where the population parameter is likely to be contained. The sample size should be appropriate for the best estimate of the population parameter.
Factors that Affect Confidence Intervals :
There are three factors that determine the size of the confidence interval for a given confidence level:
Sample size
Percentage
Population size
Sample Size :
The larger your sample size, the more sure you can be that their answers truly reflect the population. This indicates that for a given confidence level, the larger your sample size, the smaller your confidence interval. However, the relationship is not linear (i.e., doubling the sample size does not halve the confidence interval).
Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error.
Answer : "Make it bigger"
Explanation :
Sample Size: Smaller sample sizes generate wider intervals. There is an inverse square root relationship between confidence intervals and sample sizes. If you want to cut your margin of error in half, you need to approximately quadruple your sample size.
Not exactly what you’re looking for?
Ask My Question

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 2020-12-27
Consider the next 1000 98% Cis for mu that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ?
What isthe probability that between 970 and 990 of these intervals conta the corresponding value of ? (Hint: Let
Round your answer to four decimal places.)
‘the number among the 1000 intervals that contain What king of random variable s 2) (Use the normal approximation to the binomial distribution
asked 2021-01-10

The average zinc concentration recovered from a sample of measurements taken in 36 different locations in a river is found to be 2.6 grams per liter. Find the 95% confidence intervals for the mean zinc concentration in the river. Assume that the population standard deviation is 0.3 gram per liter. (Z0.025=1.96,Z0.005=2.575)

asked 2021-08-03
A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ=15
a) Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.
b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.
c) What is the effect of a larger sample size on the interval estimate?
Larger sample provides a-Select your answer-largersmallerItem 5 margin of error.
asked 2021-08-09

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 101.0 min. After​ treatment, the 13 subjects had a mean wake time of 94.6 min and a standard deviation of 24.9 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
Construct the 95% confidence interval estimate of the mean wake time for a population with the treatment.
min<μ<min ​(Round to one decimal place as​ needed.)
What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
The confidence interval ▼ does not include| includes the mean wake time of 101.0 min before the​ treatment, so the means before and after the treatment ▼ could be the same |are different. This result suggests that the drug treatment ▼ does not have | has a significant effect.

asked 2021-08-04
Let x be a binomial random variable with n=20 and p=42100.
a) Calculate the mean, variance and standard deviation of the random variable x.
b) Use the results of part a to calculate the intervals μ±σ, μ±2σ, and μ±3σ. Find the probability that an observation will fall into each of these intervals.
c) Are the results of part b consistent with Tchebysheff’s Theorem? With the Empirical Rule? Why or why not?
asked 2021-12-20
Confidence intervals, again Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true?
a) For a given sample size, reducing the margin of error will mean lower confidence.
b) For a certain confidence level, you can get a smaller margin of error by selecting a bigger sample.
c) For a fixed margin of error, smaller samples will mean lower confidence.
d) For a given confidence level, a sample 9 times as large will make a margin of error one third as big.
asked 2022-03-23
Let X1, ,Xn be a random sample from a normal distribution with known mean μ and unknown variance σ2. Three possible confidence intervals for σ2 are
a) (i=1n(XiX)2a1, i=1n(XiX)2a2)
b) (i=1n(Xiμ)2b1, i=1n(Xiμ)2b2)
c) (n(Xμ)2c1, n(Xμ)2c2)
where a1, a2, b1, b2, c1, c2 are constants.
Find values of these six constants which give confidence level 0.90 for each of the three intervals when n=10 and compare the expected widths of the tree intervels in this case
With σ2=1, what value of n is required to achieve a 90% confidence interval of expected width less than 1 in cases (b) and (c) above?