Business
Engineering
Math
Science
Social Science22. An investigator quantifies her uncertainty about the estimate of a population meanby reporting X tsx. What size confidence interval is this?
Image Transcriptionclose
22. An investigator quantifies her uncertainty about the estimate of a population mean by reporting X tsx. What size confidence interval is this?
Expert Answer
Confidence Interval:
Confidence interval is the interval estimate of the population parameter. It is the range where the population parameter value will lie in between.
The form of the confidence interval is,
CI = Point estimate ± Margin of error
The 100*(1–α)% confidence level means 100*(1–α)% of all possible sample values within the confidence interval will have the population parameter value and 100*α% of sample values within the confidence interval will not have the population parameter.
The approximate 100*(1–α)% confidence interval for the population mean will be obtained using the formula given below:
Central limit theorem:
If the sample size is large, then the sample mean will be approximately normally distributed with mean as population mean and standard deviation as (population standard deviation)/ SQRT(sample size), regardless of the distribution of the population from which the sample is taken.
In general the population standard deviation is rarely known. Hence, in practice sX-bar is used.
Therefore, the confidence interval will be defined as follows:
Obtain the cumulative probability value:
The given confidence interval for population mean is X-bar ± sX-bar.
From the given confidence interval it is known that the critical value is zα/2 = 1.
Step-by-step procedure to obtain the cumulative probability value using the MINITAB software:
- Choose Calc > Probability Distributions.
- Choose ‘Normal’ distribution.
- Select Cumulative probability.
- Enter mean as 0 and standard deviation as
- Under...
Math
Statistics
Related Statistics Q&A
Q: The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 larg...
A: (a) Level of significance:Level of significance (α) indicates the probability of rejecting null hypo...
Q: What is your favorite color? A large survey of countries, including the United States, China, Russia...
A: A).State the appropriate hypothesis:Let P be the population proportion of individuals who claim blue...
Q: Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annu...
A: Note:Hi! Thank you for posting the question. Since your question has more than 3 parts, we have solv...
Q: A political candidate has asked you to conduct a poll to determine what percentage of people support...
A: As there is no any estimates available, the sample proportion is assumed to be 0.50, that is, 50%.He...
Q: 2. Previously, you studied linear combinations of independent random variables. What happens if the ...
A: Consider the provided information:μx ≈ 7.34, σx ≈ 6.55, μy ≈ 13.19, σy ≈ 18.57, ...
Q: Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of ...
A: Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three su...
Q: The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate co...
A: Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three su...
Q: Q5. You are considering two investment choices: a. 1 year CD that pays 2% for sure; b. investing in ...
A: Portfolio Mean and SDI am answering all the sub-partsQ5. You are considering two investment choices:...
Q: Workers at a large toxic cleanup project are concerned that their white blood cell counts may have b...
A: Let the random variable X be the white blood cell count per cubic millimetre of whole blood in a hea...
