Consider a binomial process with proportion p = 1/5. Now consider the calculationof the sample proportion p = 2 where x is the number of successes and n = 40 is thenumber of trials.n(a) What is the mean of the sampling distribution for p?(b) What is the standard deviation of the sampling distribution for p?(c) Now consider doubling the number of trials to n = = 80. How does this affect themean and standard deviation of the sampling distribution for p? Do they change?If so, what are the new values? Does this lead to a better or worse estimation ofthe true proportion p?

Given: Population proportion p=15 Number of trial n=40 Sample proportion p^=xn where, x is number of…

Answered: Consider a binomial process with…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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20. Sampling distribution. From 1975 through 2016, the mean gain of the Down jones industrial average was 470. A random sample of 32 years is selected from population. What is the probability that the mean gain for the sample was between 200 and 500. The standard deviation of population is 1215
The mean weekly earnings of all female workers in a state is $710 and the mean weekly earnings of all male workers in the same state is $760. The standard deviations of the weekly earnings are $86 for the females and $106 for the males. Suppose we take one sample of 316 female workers and another sample of 329 male workers from this state. 1.1. By hand, what is the mean of the sampling distribution of the difference between the mean weekly earnings for females and males? 1.2. By hand, what is the standard deviation of the sampling distribution of the difference between the mean weekly earnings for females and males, rounded to two decimal places?
Q1. Researchers developed a "cat IQ test" and find that the population of cats in the United States has a mean score of µ = 25 on this test with a standard deviation of σ = 3. You decide to test a sample of n = 45 cats to do some research about whether some breeds are smarter. What is the expected value of the sampling distribution of the mean?
Recent studies have shown that about 16% of American adults fit the medical definition of being obese. A large medical clinic would like to estimate what percentage of their patients are obese, so they take a random sample of 400 patients and find that 52 are obese. Suppose that in truth, the same percentage holds for the patients of the medical clinic as for the general population, 16%. Find the mean of the sampling distribution of p̂.
A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 21.2 pounds and a standard deviation of 4.6 pounds. Step 1 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 85 people on this diet, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.
In a normal distribution of scores, four participants obtained the following deviation scores: +1, −2, +5, and −10. (a) Which score reflects the highest raw score? (b) Which score reflects the lowest raw score? (c) Rank-order the deviation scores in terms of their frequency, starting with the score with the lowest frequency.
What happens to the t-distribution as the sample size increases?
For a sample, a score that is 12 points above the mean has a z-score of z = 1.20. What is the sample standard deviation?
A population has a mean μ=40 and a standard deviation σ=4. What is the standard deviation of the sampling distribution of the sample means if the sample size is n=16?
Deanna is the principal at a Midwestern middle school and wants to know the average IQ of all female, seventh grade students. She does not know anything about what the population distribution looks like. She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15. Using the sample standard deviation above to estimate the population standard deviation, what is the minimum sample size needed for a 99.5% confidence interval to have a margin of error of no more than 2.3?

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