Exercises. Show all necessary solutions.1. A research worker wishes to estimate the mean of a population using a sample large enough thatthe probability will be 0.95 that the sample mean will not differ from the population mean bymore than 25 percent of the standard deviation. How large a sample should he take?2. Let X1, X2 be a random sample from N(0, 1). What is the distribution of each of the following?а. (Х2 — X1)/V2b. (X1+ X2)²/(X2 – X1)²c. (X2 + X1)//(X1 – X2)²d. X{/X?3. Derive the variance of the F distribution.4. If X has an F distribution with m and n degrees of freedom, argue that 1/X has an F distributionwith n and m degrees of freedom.5. Derive the variance of the Student's t distribution.6. If X is t-distributed, show that X? is F-distributed.

Since you have asked multiple question, we will solve first question for you. If you want any…

1. A research worker wishes to estimate the mean of a population using a sample large enough that the probability will be 0.95 that the sample mean will not differ from the population mean by more than 25 percent of the standard deviation. How large a sample should he take?

1. A research worker wishes to estimate the mean of a population using a sample large enough that the probability will be 0.95 that the sample mean will not differ from the population mean by more than 25 percent of the standard deviation. How large a sample should he take?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: The cost of textbooks is normally distributed with a mean of $203. You do not know the population…

A: Solution: Let X be the cost of textbook. From the given information, x-bar=$203, s=$48 and n=4.

Q: The mean of a population is 40 and its standard deviation is 3. What are the values of the mean…

A: Given that Mean=E(X)=40 Standard deviation=Std(X)=3 Variance=Var(X)=32=9

Q: Suppose that the population IQ scores are normally distributed with mean value 100.0 and standard…

A: For the normally distributed IQ scores, it is given that: μ=100.0 and σ=15.0. For n no. of sampled…

Q: What does a z-score of –1.5 mean? A.The mean is 1.5 standard deviations less than the measurement.…

A: 3. z-score: The z score determines how far the individual measurement is from the value of mean. If…

Q: B. Find and interpret the mean, variance, and standard deviation of the sampling distribution of…

A: Let X represents the age of employees. X is normally distributed with mean u= 47.2 and standard…

Q: Suppose a population is known to be normally distributed with a mean, equal to 116 and a standard…

A: Given dataMean = 116Standard deviation = 14Probability that population would be between 116 and 130…

Q: Suppose that you want to determine the number of people who will attend a conference this year. In…

A: Given information: The investigator wants to determine the umber of people who will attend a…

Q: An IQ test is designed so that the mean is 100 and the standard deviation is 16 for the population…

Q: If the standard deviation of the mean for the sampling distribution of random samples of size 36…

Q: 1. How much of the data lies between one standard deviation from the mean, two standard deviations…

Q: Suppose someone was diagnosed with a form of cancer that had a median survival time of eight months.…

A: Introduction: The median of a data set is a value that divides the top half (or top 50%) of the data…

Q: A simple random sample of 100 observations was taken from a large population. The sample mean and…

A: Standard error of mean=snwhere s=sample standard deviationn=sample size The standard error provides…

Q: A market researcher wants to estimate the amount of money that a Christmas shopper will spend on…

A: We have to find sample size for given data..

Q: Problem. For a standard normal distribution, find the percentage of data that are more than 2…

A: To find the given percentage.The standard Normal distribution is given below. It has mean is 0 and…

Q: Assume thAt scores on a standardized test are known to follow a bell shaped distribution with a mean…

A: L

Q: Suppose that you draw a random sample from a population where you know the population mean is 36 and…

Q: A z-score of −1 tells us that a score fell one standard deviation below the mean in a group of…

A: Empirical rule: For a normal distribution, the approximate values that fall in the specified…

Q: In a certain state, two-fifths of all adults register as Democrats. A random sample of 150 adults…

A: From the information, given thatLet the random variable X denotes the number of registered Democrats…

Q: Ex. 13. If the probability of a defective bolt is 0.2, find (i) mean (ii) standard deviation for the…

A: Givenp=0.2sample size(n)=400

Q: Find the probability that mean of sample size 36 will be negative.

Q: Suppose you know that the population variance for the weight of tractors is 4,000,000. What sample…

Q: An IQ test is designed so that the mean is 100 and the standard deviation is 17 for the population…

A: For the distribution of IQ scores for normal adults at the population level, it is given that:…

Q: How many business students must be randomly selected to estimate the mean monthly earnings of…

A: From the given information,Confidence level ,C = 0.95 Using formula,

Q: An instructor of statistics claims that students in his section will score higher than the students…

A: The random variable is score. There are two independent samples which are section and colleague’s…

Q: 2. A random sample of receipts for individuals eating at the Terrace Restaurant showed the sample…

A: Consider that a random variable X has expected value x̄ and standard deviation, s. Now, according to…

Q: Suppose that you have a distribution involving a continuous random variable x. Discuss how one…

A: It is given that there is a distribution which has a continuous random variable x.

Q: The cost of textbooks is normally distributed with a mean of $232. You do not know the population…

Q: The performance on a national standardized aptitude test in a certain professional field is reported…

Q: Test scores: Scores on a statistics exam had a mean of 84 with a standard deviation of 13. Scores on…

Q: The director of a medical hospital feels that her surgeons perform fewer operations per year than…

A: Given information- Population mean, μ=211 Sample size (n) = 15 Sample mean, X=208.8 Sample standard…

Q: For a sample with a mean if M=63, a score of X=54 corresponds to Z= -0.75. what is the sample…

A: Given,Mean(M)=63a raw score(X)=54Z-score=-0.75

Q: Answer the problem and show your solution: The IQs of Grade 11 students in Pulot National High…

A: Solution-: Given: μ=98,σ=8 We find, P( score of grade 11 students is higher than 110)=?

Q: Suppose you have the population values 50 and 80 and that their corresponding z-scores are-1 and 2.…

A: Given : Suppose the population values 50 and 80 and that their corresponding z scores are -1 and 2…

Q: . 18 For a binomiał distribution the mean is 6 and the standard deviation is V2. Write out all the…

Q: large population of 5,000 students take a practice test to prepare for a standardized test. The…

A: Population mean, Population standard deviation,

Q: A population has a mean 75 and standard deviation 12. a. A random sample of 125 are taken. Find the…

A: Given: X~N(mean=75 , standard deviation=12) n=125

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Exercises. Show all necessary solutions.
1. A research worker wishes to estimate the mean of a population using a sample large enough that
the probability will be 0.95 that the sample mean will not differ from the population mean by
more than 25 percent of the standard deviation. How large a sample should he take?
2. Let X1, X2 be a random sample from N(0, 1). What is the distribution of each of the following?
а. (Х2 — X1)/V2
b. (X1+ X2)²/(X2 – X1)²
c. (X2 + X1)//(X1 – X2)²
d. X{/X?
3. Derive the variance of the F distribution.
4. If X has an F distribution with m and n degrees of freedom, argue that 1/X has an F distribution
with n and m degrees of freedom.
5. Derive the variance of the Student's t distribution.
6. If X is t-distributed, show that X? is F-distributed.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

1.The test scores of Biostatistics examination follows a normal distribution with a mean of 60 and a standard deviation of 5. What is the standard score of those who got 50? a.1 b.-1 c.2 d.-2 2.The test scores of Biostatistics examination follows a normal distribution with a mean of 60 and a standard deviation of 5. What is the probability that the student got a score of below 55? a.0.3413 b.0.8413 c.0.1587 d.0.6587
When sampling from a population with mean μ and standard deviation σ, the sampling distribution of the mean will also have a mean μ and standard deviation σ.
A sample of n=11 scores has a mean of M=9. If one new person with a score of X=4 is added to the sample, what will be the value of the new mean?
Alex wants to find out: if the standard deviation of the mean for the sampling distribution of random samples of size 256 from a large or infinite population is 9, how large must the sample size become if the standard deviation is to be reduced to 2.7 (or even smaller)?
A sample of n = 15 scores has a mean of M = 6. One person with a score of X = 22 is added to the sample. What is the value for the new sample mean?
How can I solve?
2. The mean of a statistics examination is 77.0. a. If your score is 85, would you prefer the standard deviation to be large or small for purposes of getting a better grade? Why? b. If your score is 69, would you prefer the standard deviation to be large or small? Why?
3. A medical statistician wants to estimate average weight loss of people who are on a new diet plan. In a preliminary study, he guesses that the standard deviation of the population of weight losses σ is about 10 pounds. How large a sample should he take to estimate the mean weight loss to within 2 pounds with 95% confidence?
4. A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. In a preliminary study, he guesses that the standard deviation of weight loss is about 10 pounds. How large a sample should he take to estimate the mean weight loss to within 2 pounds, with a 90% confidence.
4. A normal population has the mean of 20 and the variance of 100. A random sample of size n = 69 is selected. (a) Find the standard deviation of the sample mean. (b) How large must the sample be if you want to halve the standard deviation of the sample mean?
4. The variance of a data set is 3410.56. Find the standard deviation for the data set. This ample of
A population has mean of 120 and standard deviation of 10. A sample of size 5015 is taken from the population. What is the mean and the standard deviation of the sampling distribution of the sample mean?