QUESTION 2a. i) Construct the sampling distribution of the mean based on all possible samples of sizen 2, drawn without replacement from a population consisting of (1, 2, 3,4}.ii) Based on your answer to part i), name with reasons the sampling procedure employed to generate the samples used todistribution of the mean.construct the samplingb. Use the sampling distribution constructed in part i) of a) to demonstrate that the sample mean and the sample variance are unbiased estimators of the populationmean and variance respectively.c. Estimate the standard error of the sample mean based on the sample (1,4), assuming that the population variance is:known.Unknown.d. Estimate the population total and its standard error based on sample (1,4).Attach FileBrowse Local Files15:4414°C4) ENGO Type here to search2021/11/26Tomle144Than%2:

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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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I need assistance with D and E Only. Given the sample data. x: 23, 17, 15, 32, 27 (a) Find the range. (Enter an exact number.) (b) Verify that Σx = 114 and Σx2 = 2,796. (For each answer, enter an exact number.)Σx = Σx2 = (c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (For each answer, enter a number. Round your answers to two decimal places.)s2 = s = (d) Use the defining formulas to compute the sample variance s2 and sample standard deviation s. (For each answer, enter a number. Round your answers to two decimal places.)s2 = s = (e) Suppose the given data comprise the entire population of all x values. Compute the population variance σ2 and population standard deviation σ. (For each answer, enter a number. Round your answers to two decimal places.)σ2 = σ =
A) A sample of n=5 scores has a mean m=12. If one score with a value x=18 is added to the sample, what is the value for the new mean? B) Find the mean for the scores in the following frequency distribution table X F 9 1 8 1 7 3 6 4 5 1 4 0 The mean to two decimal places? C) A population of N=10 scores has a mean of mu =12, if one score with a value of X= 21 is removed from the popultion, then what is the value of the new population mean?
For a population with a mean equal to 200 and a standard deviation equal to 30, calculate the standard error of the mean for the following sample sizes. a) 20 b) 40 c) 60 a) The standard error of the mean for a sample size of 20 is (Round to two decimal places as needed.) b) The standard error of the mean for a sample size of 40 is (Round to two decimal places as needed.) c) The standard error of the mean for a sample size of 60 is
QUESTION 1 a) The table below gives the frequency distribution of marks obtained by a group of students in a class test. Marks 3 4 5 6 7 8 Frequency 5 x-1 x 9 4 1 i) Find the value of x if the mean for the distribution is 5. ii) What is the modal mark. iii) Find the mean absolute deviation. iv) Find the sample variance and the sample standard deviation b) By using the phrases “correct decision” or “wrong decision”, complete the decision table for hypothesis testing below. Where the decision is wrong, state the type of error committed. DECISION H0 is false H0 is true Reject H0 Fail to Reject H0 (c) In the test of a certain hypothesis the p-value corresponding to the test statistics is 0.0316. Can the null hypothesis be rejected at the; i) 01 level of significance? ii) 05 level of significance? 10 level of significance? Justify your answers.…
A population consists of the two numbers (7, 8). Consider all possible samples ofsize 2 that can be drawn with replacement from this population. Find the following:a. The mean of the sampling distribution of meansb. The variance of the sampling distributionc. The standard deviation of the sampling distribution of means.d. Illustrate the probability histogram of the sampling distribution of themeans. The average number of liters of water that a person consumes in a month is 12 liters. Assume that the standard deviation is 4.5 liters and the distribution isapproximately normal.a. Find the probability that a person selected at random consumes morethan 13 liters per month.b. If a sample of 20 individuals is selected, find the probability that mean ofthe sample will be more than 13 liters. Identify the region under the t-distribution corresponding to the t-value which is 1.440 and the area is on both sides of the t-distribution. Identify the region under the t-distribution corresponding to…
Suppose you compile all possible samples of 25 children of preschool age in your school district. If you calculate the mean of each sample (M) and create a frequency distribution of these means, this distribution is referred to as the
Deascribe the sampling distribution of the sample proportion? A )the sampling distribution of the sample proportion for a simple random sample of size n = 167. the proportion with a specified characteristic is p=0.01. Assume that the size of the population is 1,267 B) the sampling distribution of the sample for a simple random sample n=56. the proportion with a specified characteristic is P= 0.55. assue that the size of the population is 10,4551
Suppose I want to sample the household incomes for EBR parish. Let's say I start with a simple random sample of 100 residents and calculate the sample mean. How would the sampling distribution of change if I increase the sample size to 1,000 residents?
8. This question requires you to work z score problems with the sampling distribution of means. For each problem, begin by computing the standard error of the mean, using the formula: OM Then make two diagrams of the problem-one in terms of the actual scores, and one in terms of the z scores; mark the area under investigation on each curve. Show calculation of the appropriate z scores. List the line(s) from the z score table that you use to answer the question. Provide a verbal answer to each question. a. Assume you have a sampling distribution of means of samples of size n=16 from a population distribution in which u = 46 and o = 36. What proportion of sample means fall above M = 48? b. Assume you have a sampling distribution of means of samples of size n=25 from a population distribution in which u = 100 and o = 15. What proportion of sample means fall above M = 96? c. Assume you have a sampling distribution of means of samples of size n=49 from a population distribution in which u =…
Calculating sample variance requires a slight modification in the formula as compared to calculate in population variance. Why? a) the population parameter is equal to the sample statistic b) the sample variability is too difficult to measure directly c) samples have systematically more variability than the populations from which they are drawn d) samples have systematically less variability than the populations from which they are drawn
The chromium percentages of the samples obtained from the drillings in the field are given below. Prepare the frequency table of the distribution by taking the lower limit of the first class as 20 and the class interval as 10 in the frequency table and answer the questions below a) What is the avarege of the distribution? b) What is the Standard Deviation of the Distribution? c) What is the coefficient of variation of the distribution? d) What is the median value of the distribution?

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